EXHIBIT 31.1 CERTIFICATION I, Gosse B.
Bruinsma, M.D., certify that: 1. I have reviewed this
quarterly report on Form 10-Q of Axonyx Inc.; 2. Based on my knowledge,
this 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 report; 3. Based on my knowledge,
the financial statements, and other financial information included in this
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 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-15(e)
and 15d-15(e)) and internal control over financial reporting (as defined in
Exchange Act Rules 13a-15(f) and 15d-15(f)) for the registrant and 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 report is being prepared; b)
designed such internal control over financial reporting, or caused such
internal control over financial reporting to be designed under our supervision,
to provide reasonable assurance regarding the reliability of financial
reporting and the preparation of financial statements for external purposes in
accordance with generally accepted accounting principles; c)
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 report based on such evaluation; and d)
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 (the registrants fourth fiscal quarter in the case of annual report)
that has materially affected, or is reasonably likely to materially affect, the
registrants internal control over financial reporting; and 5. The registrants other
certifying officer and I have disclosed, based on our most recent evaluation of
internal control over financial reporting, to the registrants auditors and the
audit committee of the registrants board of directors (or persons performing
the equivalent functions): a)
all significant deficiencies and material weaknesses in the design or operation
of internal control over financial reporting which are reasonably likely to
adversely affect the registrants ability to record, process, summarize and
report financial information; and b)
any fraud, whether or not material, that involves management or other employees
who have a significant role in the registrants internal control over financial
reporting. Date: August
8, 2005 /s/ Gosse B.
  Bruinsma, M.D.Gosse B. Bruinsma, M.D.President
  and Chief Executive Officer