Exhibit 99.2

MANAGEMENT’S DISCUSSION AND ANALYSIS

For the three and six months ended June 30, 2015

August 4, 2015

This Management’s Discussion and Analysis (“MD&A”) of Aptose Biosciences Inc. (“Aptose”, the “Company”, “we”, “us” and similar expressions) for the interim period should be read in conjunction with the Company’s unaudited condensed consolidated interim financial statements for the three and six months ended June 30, 2015 and the three and six months ended May 31, 2014.  The June 30, 2015 interim financial statements and additional information about the Company, including the annual audited financial statements and MD&A as at December 31, 2014 and for the seven months then ended, and the annual report on form 20-F of the Company as at December 31, 2014 and for the seven months then ended can be found on SEDAR at www.sedar.com and EDGAR at www.sec.gov/edgar.shtml.

This MD&A is prepared as of August 4, 2015. It contains certain forward-looking statements that involve known and unknown risks and uncertainties which are beyond the control of the Company. This MD&A should be read in conjunction with the unaudited condensed consolidated interim financial statements of the Company for the three and six months ended June 30, 2015 which are incorporated by reference herein and form an integral part of this MD&A.

Effective July 17, 2014 the Company changed its fiscal year end from May 31 to December 31. As a result of that change, the current interim period being reported is for the three and six months ended June 30, 2015, while the prior year comparative period is for the three and six months ended May 31, 2014.

CAUTION REGARDING FORWARD-LOOKING STATEMENTS

This management’s discussion and analysis may contain forward-looking statements within the meaning of securities laws. Such statements include, but are not limited to, statements relating to:

The forward-looking statements reflect our current views with respect to future events, are subject to risks and uncertainties, and are based upon a number of estimates and assumptions that, while considered reasonable by us, are inherently subject to significant business, economic, competitive, political and social uncertainties and contingencies. Many factors could cause our actual results, performance or achievements to be materially different from any future results, performance, or achievements that may be expressed or implied by such forward-looking statements, including, among others:

Should one or more of these risks or uncertainties materialize, or should the assumptions set out in the section entitled “Risk Factors” underlying those forward-looking statements prove incorrect, actual results may vary materially from those described herein. These forward-looking statements are made as of the date of this management’s discussion and analysis or, in the case of documents incorporated by reference herein, as of the date of such documents, and we do not intend, and do not assume any obligation, to update these forward-looking statements, except as required by law. We cannot assure you that such statements will prove to be accurate as actual results and future events could differ materially from those anticipated in such statements. Investors are cautioned that forward-looking statements are not guarantees of future performance and accordingly investors are cautioned not to put undue reliance on forward-looking statements due to the inherent uncertainty therein.

corporate update

Orphan Drug Designation

On June 2, 2015 we announced that the U.S. Food and Drug Administration (“FDA”) had granted Aptose orphan drug designation for APTO-253 for the treatment of acute myeloid leukemia (“AML”). APTO-253, a first-in-class inducer of the Krüppel-like factor 4 (“KLF4”) gene, is the Company’s lead product candidate in a Phase Ib clinical trial in patients with AML, high-risk myelodysplastic syndrome (“MDS”) and other hematologic malignancies in which KLF4 silencing is reported as operative.

Orphan drug designation is granted by the FDA to encourage companies to develop therapies for the treatment of diseases that affect fewer than 200,000 individuals in the United States. Orphan drug status provides research and development tax credits, an opportunity to obtain grant funding, exemption from FDA application fees and other benefits. If APTO-253 is approved to treat AML, the orphan drug designation provides Aptose with seven years of marketing exclusivity.

At The Market Facility

In early April, Aptose entered into an at-the-market (“ATM”) facility for up to US $20,000,000. The ATM will, along with the effective shelf prospectus that was filed in December 2014, provide us with the added flexibility to quickly access the market and raise capital at market price without the need to undertake a larger, more dilutive offering.

program updates

APTO-253

Preclinical and Phase I Solid Tumor Trial

We have submitted an abstract for presentation at the 2015 American Society of Hematology (“ASH) Meeting with further insights into the preclinical and clinical pharmacology and pharmacokinetics of APTO-253. This abstract submission will include data from the prior Phase 1 clinical trial in patients with solid tumors.

Phase Ib Hematologic Malignancy Trial

On July 28, 2014 we announced that the FDA had completed its review and cleared the Investigational New Drug (“IND”) application of APTO-253 for the treatment of hematologic malignancies, including AML, MDS, lymphomas and multiple myeloma. Clearance of the IND allowed us to initiate a Phase Ib, multi-center, open-label, clinical study of APTO-253 in patients with relapsed or refractory hematologic malignancies. The trial is expected to enroll 45-60 patients as part of a dose-escalation program and two separate disease-specific single-agent expansion cohorts.

The dose escalation study includes two separate arms: one group of up to 15 patients dedicated to AML and high-risk MDS and another group of up to 15 patients for lymphomas and multiple myelomas. The two separate arms will allow for a focused look at AML and high-risk MDS and exploration of the effect of APTO-253 on lymphomas and myelomas. They will also potentially provide patient data on up to two times the number of patients than would have been possible with only a single arm study. We have enrolled patients on both arms of the trial.

The primary objectives of the Phase Ib trial are: (i) to further assess safety on an optimized dosing schedule versus the prior Phase 1 solid tumor trial, and (ii) to identify the recommended dose for APTO-253 for the upcoming Phase Ib single-agent expansion and Phase 2 combination trials. The Phase 1b expansion studies will include up to 15 patients each in dedicated AML and MDS cohorts..

In the Phase 1b dose escalation portion of the study, we plan to monitor levels of KLF4 and the product of the embryonic gene Cdx2, the protein CDX2 (“CDX2”), upon entry, in patients throughout the study, and during a post-treatment period. We will not exclude patients based on KLF4 or CDX2 status from participating in this first study as we believe this approach may be useful in further validating our companion diagnostic and observing potential responses among the broader population. Subsequent to the dose escalation portion of the Phase 1b study, we plan on screening patients in the expansion portions of the trial, and in the Phase 2 combination trials, for levels of KLF4 and CDX2 anticipated to confer maximal sensitivity to APTO-253.

On January 13, 2015 we announced that we had dosed the first patient in the Phase Ib dose-escalation study at Baylor Cancer Center in Dallas. During the three months ended March 31, 2015 we added three additional sites at MD Anderson Cancer Center in Houston, Oregon Health & Sciences University (“OHSU”) and the University of Michigan. We expect to add two additional sites in the quarter ended September 30, 2015 and will continue to seek to add additional high quality institutions as clinical sites.

At this point in time, we have dosed patients at the 20mg/m2, 40mg/m2 and 66 mg/m2s dose levels of APTO-253. Patients are being dosed on a schedule in which they receive APTO-253 on days 1 and 2 of each week of a 28 day cycle, and their bone marrow and peripheral blood samples are being collected and processed for biomarker analysis.  The next dose level is 100mg/m2. Based on our preclinical data with heme cancer cells and our prior clinical experience using a different dosing schedule, we believe that we may be entering the therapeutic range for heme cancer patients at the 100mg/m2 dose level. 

We anticipate providing a potential update on the dose-escalation study findings at, or around the timing of the American Society of Hematology (“ASH”) Meeting in December 2015, completing enrollment of the Phase Ib dose-escalation study by late-2015 or the first half of 2016, starting the single agent expansion and Phase 2 combination studies in 2016.

Beat AML Initiative

In parallel to the single agent dose escalating Phase Ib trial with APTO-253, we have been performing studies through the Beat AML Initiative, a groundbreaking initiative that was formed in collaboration with The Leukemia & Lymphoma Society and the Knight Cancer Institute at OHSU to better understand AML. Beat AML is designed to leverage the expertise of functional genomic technologies and pharmaceutical collaborators to take a next-generation personalized medicine approach to improve outcomes for AML patients. Our efforts with the Beat AML initiative, and with Dr. Brian Druker and his group at OHSU, have allowed us to evaluate the effect of APTO-253 as a monotherapy and in combination with other anti-cancer agents. APTO-253 has been evaluated against a large number of fresh bone isolates from patients with AML, MDS, chronic myeloid leukemia (“CML”) and chronic lymphocytic leukemia (“CLL”). In addition, genomic sequencing of these primary isolates is helping to provide a rationale for APTO-253 for use as a single agent or in drug combination against specific hematologic malignancies.

We undertook these studies to confirm the strong preclinical efficacy observed across a range of hematologic cell lines.  An additional reason for these studies is to identify drug combinations that could offer improved risk-benefit outcomes.  Dr. Brian Druker’s group at OHSU has submitted an abstract of these findings for presentation at the ASH Meeting in December 2015.  Importantly, these findings may be used to guide the design of our anticipated drug combination trials with APTO-253.

financing activities

During the six months ended June 30, 2015 we received cash proceeds of $848 thousand related to stock option and warrant exercises.

LIQUIDITY AND CAPITAL RESOURCES

Since its inception, Aptose has financed its operations and technology acquisitions primarily from equity and debt financing, proceeds from the exercise of warrants and stock options, and interest income on funds held for future investment.

We currently do not earn any revenues from our drug candidates and are therefore considered to be in the development stage. The continuation of our research and development activities and the commercialization of the targeted therapeutic products are dependent upon our ability to successfully finance and complete our research and development programs through a combination of equity financing and payments from strategic partners. We have no current sources of significant payments from strategic partners. We currently believe we have capital resources sufficient to fund our research and development and operations into early 2017.

Cash Position

At June 30, 2015, we had cash and cash equivalents and investments of $25.2 million compared to $30.5 million at December 31, 2014. We generally invest our cash in excess of current operational requirements in highly rated and liquid instruments. Investment decisions are made in accordance with an established investment policy administered by senior management and overseen by our Board of Directors. As at June 30, 2015 our cash and cash equivalents consisted of cash of $2.748 million (December 31, 2014 - $293 thousand) and funds in both Canadian and US dollars deposited into high interest savings accounts totaling $14.296 million (December 31, 2014 - $14.072 million). Working capital (representing primarily cash, cash equivalents, investments and other current assets less current liabilities) at June 30, 2015 was $24.5 million (December 31, 2014 –$29.1 million).

We do not expect to generate positive cash flow from operations for the foreseeable future due to additional research and development costs, including costs related to drug discovery, preclinical testing, clinical trials, manufacturing costs and operating expenses associated with supporting these activities. It is expected that negative cash flow will continue until such time, if ever, that we receive regulatory approval to commercialize any of our products under development and/or royalty or milestone revenue from any such products exceeds expenses.

RESULTS OF OPERATIONS

Our net loss for the three months ended June 30, 2015 was $3.4 million ($0.28 per share) compared with $4.2 million ($0.49 per share) during the three months ended May 31, 2014. Net loss for the six months ended June 30, 2015 was $6.9 million ($0.59 per share) compared with $6.7 million ($0.97 per share) during the six months ended May 31, 2014.

The decrease in net loss during the three months ended June 30, 2015 in comparison to the three months ended May 31, 2014 is due to lower general and administrative costs resulting from lower legal and patent costs, lower Board fees and severance costs incurred in the prior year related to our former President and COO as well as increased finance income in the current year quarter related to a gain on US dollar cash balances during the period. These decreases were partially offset by higher research and development costs in the current year associated with increased clinical activity on APTO-253 and associated activities.

The increase in net loss during the six months ended June 30, 2015 compared with the six month period ended May 31, 2014 is due to higher research and development activities associated with the development of APTO-253 as well as higher general and administrative costs related to higher stock based compensation expense, our NASDAQ listing and related expenses and clean-up and moving costs related to the Toronto office and lab relocation. These increase expenditures were partially offset by increased finance income associated with foreign currency gains on our US dollar cash balances.

We utilized cash of $4.3 million in our operating activities in three-month period ended June 30, 2015 compared with $3.9 million during the three months ended May 31, 2014. For the six months ended June 30, 2015 we utilized cash of $6.5 million compared with $6.1 million in the six months ended May 31, 2014. The cash utilized in the three month period is higher than the three months ended May 31, 2014 despite a lower net loss due to cash used to reduce accounts payable and accrual balances in the current year period.

At June 30, 2015, we had cash and cash equivalents and investments of $25.2 million compared to $30.5 million at December 31, 2014.

Research and Development

Research and development expenses totaled $1.3 million in the three months ended June 30, 2015 compared to $1.0 million during the three months ended May 31, 2014 and totaled $2.2 million for the six month period ended June 30, 2015 compared with $1.6 million in the six months ended May 31, 2014. Research and development costs consist of the following:

Components of research and development expenses:

Research and development costs in the three months ended June 30, 2015 increased compared with the three months ended May 31, 2014 primarily due to increased APTO-253 development costs including the ongoing Phase 1b clinical trial of APTO-253 in the current year period compared with no ongoing clinical development in the prior year period. In addition we have initiated studies to optimize the formulation of APTO-253 for which no comparable work was ongoing in the prior year period. Increased program expenditures were partially offset by no severance costs in the three months ended June 30, 2015 compared with $326 thousand in the three months ended May 31, 2014 related to severance payments made to our former President and COO. There were no deferred share units outstanding in the three months ended June 30, 2015 compared with a reduction in the fair value of units outstanding in the three months ended May 31, 2014.

The increase in research and development costs during the six months ended June 30, 2015 is the result of increased APTO-253 development costs primarily related to the ongoing Phase 1b clinical trial and associated activities including formulation studies and research support. Increased program expenditures were offset by no severance costs in the six months ended June 30, 2015 compared with $326 thousand in the six months ended May 31, 2014 related to severance payments made to our former President and COO.

We anticipate an increase in research and development costs in the second half of 2015 due to the continuation of our Phase 1b clinical trial.

General and Administrative

General and administrative expenses totaled $2.5 million in the three-month period ended June 30, 2015 compared to $3.2 million in the three months ended May 31, 2014. For the six month period ended June 30, 2015, general and administrative expenses were $5.2 million compared with $5.0 million in the six months ended May 31, 2014. General and administrative expenses consist of the following:

Components of general and administrative expenses:

General and administrative expenses excluding salaries decreased in the three months ended June 30, 2015 compared with the three months ended May 31, 2014. The decrease over the prior year is attributable to lower legal and patent costs and lower Board fees due to a change in annual payment structure.

General and administrative expenses excluding salaries increased in the six months ended June 30, 2015 compared with the six months ended May 31, 2014. The decreases incurred in the three months ended June 30, 2015 were partially offset by higher expenses in the three months ended March 31, 2015 related to our NASDAQ listing and related expenses and clean-up and moving costs related to the Toronto office and lab relocation.

Salary charges in the three and six months ended June 30, 2015 were consistent with the three and six month periods ended May 31, 2014 as staffing levels were consistent year over year.

Severance costs were incurred in the three and six months ended May 31, 2014 as our former President and COO left in March 2014. There are no ongoing costs related to the severance payments.

Stock-based compensation costs increased in both the three and six months ended June 30, 2015 compared with the three month and six months ended May 31, 2014 due to large option grants in April, June and July 2014 which vest 50% during the first year and therefore contribute to higher stock based compensation expense during the first twelve month period.

Deferred share unit costs relate to the marked to market adjustment on units which were settled in April 2014. There were no deferred share units outstanding in the six month period ending June 30, 2015.

Finance Expense

Finance expense for the three months ended June 30, 2015 was $15 thousand compared with $78 thousand for the three months ended May 31, 2014 and $35 thousand for the six months ended June 30, 2015 compared with $176 thousand for the six months ended May 31, 2014. Finance expense includes the following items:

Finance expense for the three and six months ended June 30, 2015 relates to interest expense of $15 thousand accrued at a rate of 10% on the remaining balance of convertible promissory notes issued in September 2013 as well as accretion expense related to the conversion feature of the notes.

Finance expense for the three and six months ended May 31, 2014 relates to interest accrued at a rate of 10% as well as accretion expense on the $918 thousand promissory notes issued in June 2013 and repaid in April 2014 as well as interest on the convertible promissory notes issued in September 2013 as described above.

Foreign exchange loss is the result of the fluctuation of rates of exchange between US and Canadian dollars.

Finance Income

Finance income totaled $462 thousand in the three months ended June 30, 2015 compared to $61 thousand in the three months ended May 31, 2014 and $526 thousand in the six months ended June 30, 2015 compared with $74 thousand in the six months ended May 31, 2014. Finance income includes the following items:

Interest income represents interest earned on our cash and cash equivalent and investment balances. Foreign exchange gain is the result of an increase in the value of our US dollar denominated cash and cash equivalents balances during the three and six months ended June 30, 2015 due to a depreciation of the Canadian dollar compared to the US dollar.

Net loss for the period

For the reasons discussed above, our net loss for the three months ended June 30, 2015 decreased to $3.4 million ($0.28 per share) compared to $4.2 million ($0.49 per share) in the three months ended May 31, 2014 and increased in the six months ended June 30, 2015 to $6.9 million ($0.59 per share) from $6.7 million ($0.97 per share) in the six months ended May 31, 2014.

QUARTERLY FINANCIAL INFORMATION (UNAUDITED)

The selected financial information provided below is derived from our unaudited quarterly financial statements for each of the last eight quarters.

Research and development expenditures were lower in the quarters ended August 31, 2013, November 30, 2013 and February 28, 2014 as the Company focused its efforts on a strategic review and securing adequate financing for future development. In the quarter ended May 31, 2014, expenditures increased due to the allocation of severance costs related to the former President and COO of the Company to research and development of $326 thousand. In the four months ended September 30, 2014 and in following quarters, research and development activities increased as we prepared and subsequently launched the APTO-253 Phase Ib clinical trial.

The increased general and administrative expense in the three months ended November 30, 2013 is due to stock option grants during the quarter which vested immediately and resulted in higher than normal stock-based compensation expense. In addition costs associated with hiring new executives during the quarter ended November 30, 2013 increased salary-related costs. In the three months ended February 28, 2014, general and administrative expenses were higher due to additional members of management and bonuses as well as increased travel, consulting and legal costs and general and administrative costs continued to trend upwards in calendar 2014 due to additional salary costs and increased levels of corporate activities.

The increase in general and administrative expense in the three months ended May 31, 2014 is due to severance costs associated with the former President and COO of the Company ($762 thousand), bonus costs, and increased Board, consulting and legal fees associated with activities during the quarter. In the four months ended September 30, 2014, the general and administrative expense is higher due to a four-month vs. three-month period in relation to the change in the financial year of the Company discussed above as well as option grants during the quarter which increased option-related expenses. During the three months ended December 31, 2014, we incurred additional expenses related to our listing on NASDAQ and recognized an increase in expected costs to terminate our current Toronto lease which led to higher general and administrative expenses in the quarter. General and administrative costs in the three months ended March 31, 2015 again were higher due to the relocation of the Toronto office and related clean-up costs as well as costs related to our NASDAQ listing.

Cash used in operating activities fluctuates significantly due primarily to timing of payments and increases and decreases in the accounts payables and accrued liabilities balances.

Contractual Obligations and Off-Balance Sheet Financing

At June 30, 2015, we had contractual obligations requiring annual payments as follows:

The Company has entered into various contracts with service providers with respect to the clinical development of APTO-253. These contracts could result in future payment commitments of up to approximately $2.1 million over the related service period. Of this amount, $172 thousand has been paid and $111 thousand has been accrued at June 30, 2015. The payments are based on services performed and amounts may be higher or lower based on actual services performed.

As at June 30, 2015, we have not entered into any off-balance sheet arrangements other than the operating leases for our offices and labs and certain office equipment.

RISK FACTORS

Before making an investment decision with respect to our common shares, you should carefully consider the following risk factors, in addition to the other information included or incorporated by reference into this report. The risks set out below are not the only risks we face. If any of the following risks should be realized, our business, financial condition, prospects or results of operations would likely suffer. In that case, the trading price of our common shares could decline and you may lose all or part of the money you paid to buy our common shares.

Please refer to our December 31, 2014 MD&A for a complete discussion of risks and uncertainties.

Financial instruments

(a) Financial instruments

We have classified our financial instruments as follows:

At June 30, 2015, there are no significant differences between the carrying values of these amounts and their estimated market values due to their short-term nature.

(b) Financial risk management

We have exposure to credit risk, liquidity risk and market risk. Our Board of Directors has the overall responsibility for the oversight of these risks and reviews our policies on an ongoing basis to ensure that these risks are appropriately managed.

(i) Credit risk

Credit risk is the risk of financial loss to us if a customer, partner or counterparty to a financial instrument fails to meet its contractual obligations, and arises principally from our cash and cash equivalents and investments. The carrying amount of the financial assets represents the maximum credit exposure.

We manage credit risk for our cash and cash equivalents by maintaining minimum standards of R1-low or A-low investments and we invest only in highly rated Canadian corporations with debt securities that are traded on active markets and are capable of prompt liquidation.

(ii) Liquidity risk

Liquidity risk is the risk that we will not be able to meet our financial obligations as they come due. To the extent that we do not believe we have sufficient liquidity to meet our current obligations, the Board considers securing additional funds through equity, debt or partnering transactions. We manage our liquidity risk by continuously monitoring forecasts and actual cash flows. All of our financial liabilities are due within the current operating period.

(iii) Market risk

Market risk is the risk that changes in market prices, such as interest rates, foreign exchange rates and equity prices will affect our income or the value of our financial instruments.

We are subject to interest rate risk on our cash and cash equivalents however we do not believe that the results of operations or cash flows would be affected to any significant degree by a sudden change in market interest rates relative to interest rates on the investments, owing to the relative short-term nature of the investments. We do not have any material interest bearing liabilities subject to interest rate fluctuations.

Currency risk is the risk that future cash flows of a financial instrument will fluctuate because of changes in foreign exchange rates. We are exposed to currency risk from employee costs as well as the purchase of goods and services primarily in the U.S. and on cash held in foreign currencies. Fluctuations in the US dollar exchange rate could potentially have a significant impact on the Company’s results. Assuming all other variables remain constant, a 10% depreciation or appreciation of the Canadian dollar against the U.S. dollar would result in an increase or decrease in loss for the year and comprehensive loss of US$1.0 million (December 31, 2014- US$58 thousand). Balances in foreign currencies at June 30, 2015 are as follows:

We do not have any forward exchange contracts to hedge this risk and we do not invest in equity instruments of other corporations.

(c) Capital management

Our primary objective when managing capital is to ensure that we have sufficient cash resources to fund our development activities and to maintain our ongoing operations. To secure the additional capital necessary to pursue these plans, we may attempt to raise additional funds through the issuance of equity or by securing strategic partners.

We include cash and cash equivalents and short-term deposits in the definition of capital.

We are not subject to externally imposed capital requirements and there has been no change with respect to the overall capital management strategy during the three and six months ended June 30, 2015.

Related Party Transactions

In March 2015, the Company entered into an agreement with the Moores Cancer Center at the University of California San Diego (UCSD) to provide pharmacology lab services to the Company. Dr. Stephen Howell is the Acting Chief Medical Officer of Aptose and is also a Professor of Medicine at UCSD and will be overseeing the laboratory work. The research services will be provided from April 1, 2015 to March 31, 2016 for an annual fee of USD$154,456 to be paid to UCSD in monthly installments.

This transaction is in the normal course of business and will be measured at the exchange amount, which is the

amount of consideration established and agreed to by the related parties.

use of proceeds

The following table provides an update on the anticipated use of proceeds raised in the December 2013 and April 2014 equity offerings along with amounts actually expended.

As of June 30, 2015 the following expenditures have been incurred:

We currently anticipate that the total direct costs associated with the Phase Ib trial will range between $3.05 million and $3.35 million as opposed to the previously disclosed amount of approximately $1.75-2.0 million. The variance is due to the addition of a separate dose escalation arm to the Phase Ib clinical trial with lymphoma and myeloma patients.

We do not anticipate initiating the Phase 2 trials until the results of the Phase Ib are available and only then if the results warrant further clinical investigation. It is currently anticipated that the remaining balances of the research and development programs and general and corporate costs will be allocated in accordance with the previously disclosed use of proceeds.

Evaluation of DISCLOSURE CONTROLS AND INTERNAL CONTROLS

There have been no changes in the Company’s internal control over financial reporting that occurred during the three months ended June 30, 2015 that have materially affected or are reasonably likely to materially affect the Company’s internal controls over financial reporting.

UPDATED SHARE INFORMATION

As at August 4, 2015, we had 11.9 million common shares issued and outstanding. In addition there were 1.7 million common shares issuable upon the exercise of outstanding stock options and a total of 139 thousand common shares issuable upon the exercise of common share purchase warrants and promissory notes with a face value of $288 thousand which could be converted into 80 thousand common shares of Aptose at $3.60 per share.

ADDITIONAL INFORMATION

Additional information relating to Aptose, including Aptose' December 31, 2014 annual report on form 20-F and other disclosure documents, are available on SEDAR at www.sedar.com and on EDGAR at www.sec.gov/edgar.shtml.

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