|EXHIBIT 31(b)


CERTIFICATION


I, S. Colin Neill certify that:


1.  I have reviewed this quarterly
report on Form 10-Q of Axonyx Inc.;


2. Based on my knowledge,  this
quarterly  report does not contain any untrue  statement of a material fact or omit  to
state a material fact  necessary to make the  statements  made, in light of the
circumstances  under which such  statements were made, not misleading with respect to the
period covered by this quarterly report;


3. Based on my knowledge,  the
financial  statements,  and other financial  information  included in this quarterly
report,  fairly present in all material respects the financial  condition,  results of
operations and cash flows of  the registrant as of, and for, the periods presented in
this quarterly report;


4. The  registrants  other
certifying  officer and I are responsible for  establishing and maintaining  disclosure
controls and procedures (as defined in Exchange Act Rules 13a-14 and 15d-14) for the
registrant and we have:


a)
designed such  disclosure  controls and procedures,  or caused such  disclosure  controls
and procedures to be  designed under our  supervision,  to ensure that material
information  relating to the  registrant,  including its  consolidated subsidiaries,  is
made known to us by others within those entities,  particularly during the period in
which this quarterly report is being prepared; and


b)
evaluated the  effectiveness  of the  registrants  disclosure  controls and
procedures and presented in this  report our conclusions  about the  effectiveness  of
the disclosure  controls and procedures,  as of the end of the  period covered by this
quarterly report based on such evaluation (the Evaluation Date); and


c)
disclosed  in this report any change in the  registrants  internal  control over
financial  reporting  that  occurred during the registrants most recent fiscal
quarter that has materially  affected,  or is reasonably likely  to affect, the registrants
internal control over financial reporting.


5. The registrants other
certifying  officers and I have disclosed,  based on our most recent  evaluation,  to the
registrants  auditors  and the audit  committee of  registrants  board of
directors  (or persons  performing  the  equivalent function):


a)
all significant  deficiencies in the design or operation of internal  controls which are
reasonably  likely to  adversely  affect the  registrants  ability to  record,
process,  summarize  and report  financial  data and have  identified for the registrants
auditors any material weaknesses in internal controls; and


b)
any fraud,  whether or not material,  that involves  management or other employees who
have a significant role  in the registrants internal controls; and


6. The  registrants  other
certifying  officer and I have indicated in this quarterly report whether or not there
were  significant  changes in internal  controls  or in other  factors  that could
significantly  affect  internal  controls  subsequent to the date of our most recent
evaluation,  including any  corrective  actions with regard to  significant deficiencies
and material weaknesses.


Date:  May 14, 2004

/s/ S. Colin Neill
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S. Colin Neill
Chief Financial Officer, Secretary and Treasurer
(Principal Financial and Accounting Officer)
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