April 3, 2019

Gregory Chow
Senior Vice President and Chief Financial Officer
Aptose Biosciences Inc.
251 Consumers Road, Suite 1105
Toronto, Ontario, Canada M2J 4R3

       Re: Aptose Biosciences Inc.
           Form 10-K for the Fiscal Year Ended December 31, 2018
           Filed March 12, 2019
           File No. 001-32001

Dear Mr. Chow:

       We have limited our review of your filing to the financial statements
and related
disclosures and have the following comment.

       Please respond to the comment within ten business days by providing the
requested
information or advise us as soon as possible when you will respond. If you do
not believe our
comment applies to your facts and circumstances, please tell us why in your
response.

       After reviewing your response to the comment, we may have additional
comments.

Form 10-K for the Fiscal Year Ended December 31, 2018

Item 9A. Controls and Procedures, page 44

1.     Please revise to include the disclosures required by Item 307 of
Regulation S-K. Please
       also tell us how the omission of these required disclosures impacts your
conclusion with
       respect to the effectiveness of disclosure controls and procedures as of
December 31,
       2018.
 Gregory Chow
FirstName LastNameGregory Chow
Aptose Biosciences Inc.
Comapany NameAptose Biosciences Inc.
April 3, 2019
Page 3,
April 2 2019 Page 2
FirstName LastName
       In closing, we remind you that the company and its management are
responsible for the
accuracy and adequacy of their disclosures, notwithstanding any review,
comments, action or
absence of action by the staff.

      You may contact Mary Mast at (202) 551-3613 or Angela Connell at (202)
551-
3426 with any questions.



                                                          Sincerely,

                                                          Division of
Corporation Finance
                                                          Office of Healthcare
& Insurance