January 6, 2020

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

       Re: Aptose Biosciences Inc.
           Registration Statement on Form S-3
           Filed December 27, 2019
           File No. 333-235730

Dear Mr. Chow:

       This is to advise you that we have not reviewed and will not review your
registration
statement.

        Please refer to Rules 460 and 461 regarding requests for acceleration.
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.

       Please contact Ada D. Sarmento at 202-551-3798 with any questions.



                                                            Sincerely,

                                                            Division of
Corporation Finance
                                                            Office of Life
Sciences
cc:    Daniel M. Miller, Esq.