|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:  August 11, 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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