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|EXHIBIT 32.1
        CERTIFICATION PURSUANT TO18 U.S.C. SECTION 1350,AS ADOPTED PURSUANT TOSECTION 906 OF THE SARBANES-OXLEY ACT OF 2002
        In connection with the quarterly report of Axonyx Inc. (the Company) on Form 10-Q for the period ended March 31, 2005 as filed with the Securities and Exchange Commission (the Report), I, Gosse B. Bruinsma, M.D, President and Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. section 1350, as adopted pursuant to section 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:
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| | 1. | the Report fully complies with the requirements of section 13(a) of the Securities Exchange Act of 1934; and                                        
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| | 2. | the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

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|                                      | /s/ Gosse B. Bruinsma, M.D.
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|                                      | Gosse B. Bruinsma, M.D     
|President and Chief Executive Officer

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|May 10, 2005
        A signed original of this written statement required by Section 906, or other document authenticating, acknowledging, or otherwise adopting the signature that appears in typed form within the electronic version of this written statement required by Section 906, has been provided to the Company and will be retained by the Company and furnished to the Securities and Exchange Commission or its staff upon request.

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