SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                  SCHEDULE 13G
                                 (Rule 13d-102)

             INFORMATION TO BE INCLUDED IN STATEMENTS FILED PURSUANT
          TO RULES 13d-1 (b) (c), AND (d) AND AMENDMENTS THERETO FILED
                           PURSUANT TO RULE 13d-2 (b)

                               (Amendment No. 1)*

                                  Axonyx, Inc.
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                                (Name of Issuer)

                     Common Stock, $.001 par value per share
--------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                    05461R101
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                                 (CUSIP Number)

                                December 31, 2003
--------------------------------------------------------------------------------
             (Date of Event which Requires Filing of this Statement)

Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:

      |_|   Rule 13d-1(b)
      |X|   Rule 13d-1(c)
      |_|   Rule 13d-1(d)

* The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter
disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).



CUSIP No. 05461R101                    13G                     Page 2 of 6 Pages
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1.    NAME OF REPORTING PERSONS
      S.S. OR I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS

      Joseph Edelman
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2.    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS):
                                                                         (a) [_]
                                                                         (b) [X]

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3.    SEC USE ONLY


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4.    CITIZENSHIP OR PLACE OF ORGANIZATION

      United States
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               5.    SOLE VOTING POWER

                     237,367
               -----------------------------------------------------------------
  NUMBER OF    6.    SHARED VOTING POWER
   SHARES
 BENEFICIALLY        0
  OWNED BY     -----------------------------------------------------------------
    EACH       7.    SOLE DISPOSITIVE POWER
  REPORTING
   PERSON            237,367
    WITH       -----------------------------------------------------------------
               8.    SHARED DISPOSITIVE POWER

                     0
--------------------------------------------------------------------------------
9.    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

      237,367
--------------------------------------------------------------------------------
10.   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
      (SEE INSTRUCTIONS)
                                                                             [_]

--------------------------------------------------------------------------------
11.   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

      0.71%
--------------------------------------------------------------------------------
12.   TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

      IN
--------------------------------------------------------------------------------


                               Page 2 of 6 Pages


Item 1.

      (a)   Name of Issuer.

            Axonyx Inc.

      (b)   Address of Issuer's Principal Executive Offices.

            500 Seventh Avenue
            10th Floor
            New York, New York 10018

Item 2.

      (a)   Name of Person Filing.

            This Schedule 13G is being filed with respect to shares of Common
            Stock of the Issuer which are beneficially owned by Joseph Edelman.
            See Item 4 below.

      (b)   Address of Principal Business Office or, if none, Residence.

            The principal business address of the reporting person is:

            c/o First New York Securities, LLC
            850 Third Avenue, 8th Floor
            New York, NY 10022

      (c)   Citizenship.

            Mr. Edelman is a United States citizen.

      (d)   Title of Class of Securities.

            Common Stock, $0.01 par value per share

      (e)   CUSIP Number.

            05461R101


                               Page 3 of 6 Pages


Item 3. If this statement is filed pursuant to Rule 13d-1(b) or 13d-2(b) or (c),
        check whether the person filing is a:

      (a)  |_|  Broker or dealer registered under Section 15 of the Act.
      (b)  |_|  Bank as defined in Section 3(a)(6) of the Act.
      (c)  |_|  Insurance Company as defined in Section 3(a)(19) of the Act.
      (d)  |_|  Investment Company registered under Section 8 of the Investment
                Company Act.
      (e)  |_|  Investment Adviser in accordance with Sec.
                240.13d-1(b)(1)(ii)(E).
      (f)  |_|  Employee Benefit Plan or Endowment Fund in accordance with Sec.
                240.13d"1(b)(1)(ii)(F).
      (g)  |_|  Parent holding company, in accordance with Sec.
                240.13d-1(b)(ii)(G).
      (h)  |_|  A savings association as defined in Section 3(b) of the Federal
                Deposit Insurance Act.
      (i)  |_|  A church plan that is excluded from the definition of an
                investment company under Section 3(c)(14) of the Investment
                Company Act of 1940.
      (j)  |_|  Group, in accordance with Sec. 240.13d-1(b)(1)(ii)(J).

      If this statement is filed pursuant to Sec. 240.13d-1(c), check this box
      |X|.

Item 4. Ownership

      (a)   Amount Beneficially Owned.

                  237,367 (comprised of (i) 133,245 shares and warrants to
                  purchase 66,622 shares held by Mr. Edelman and (ii) warrants
                  to purchase 37,500 shares held by Perceptive Life Sciences
                  Master Fund Ltd., a Cayman Island company of which the
                  investment manager is Perceptive Advisors LLC, a Delaware
                  limited liability company of which Mr. Edelman is the managing
                  member).

      (b)   Percent of Class.           0.71%

      (c)   Number of shares as to which each such person has

            (i)   sole power to vote or to direct the vote:              237,367

            (ii)  shared power to vote or to direct the vote:                  0

            (iii) sole power to dispose or to direct the disposition of: 237,367

            (iv)  shared power to dispose or to direct the disposition of:     0


                               Page 4 of 6 Pages


Item 5. Ownership of Five Percent or Less of a Class.

      If this statement is being filed to report the fact that as of the date
      hereof the reporting person has ceased to be the beneficial owner of more
      than five percent of the class of securities, check the following |X|

Item 6. Ownership of More than Five Percent on Behalf of Another Person.

      Other persons have the right to receive and the power to direct the
      receipt of dividends from, and the proceeds from the sale of, certain of
      the shares reported herein. In that regard, Mr. Edelman is the managing
      member of Perceptive Advisors LLC, the investment manager of Perceptive
      Life Sciences Master Fund Ltd. ("Perceptive"). Accordingly, Perceptive has
      the right to receive and the power to direct the receipt of, dividends and
      the proceeds from the sale of the shares reported herein that are held by
      Perceptive.

Item 7. Identification and Classification of the Subsidiary Which Acquired the
        Security Being Reported on by the Parent Holding Company or Control
        Person.

      See Item 4(a) above, which is incorporated by reference herein.

Item 8. Identification and Classification of Members of the Group.

      Not applicable.

Item 9. Notice of Dissolution of Group.

      Not applicable.


                               Page 5 of 6 Pages


Item 10. Certification.

      By signing below I certify that, to the best of my knowledge and belief,
the securities referred to above were not acquired and are not held for the
purpose of or with the effect of changing or influencing the control of the
issuer of the securities and were not acquired and are not held in connection
with or as a participant in any transaction having that purpose or effect.

                                    SIGNATURE

      After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.

Date: February 5, 2004


                                                          /s/ Joseph Edelman
                                                       -------------------------
                                                           Joseph Edelman

      Attention: Intentional misstatements or omissions of fact constitute
Federal criminal violations (see 18 U.S.C. 1001).


                               Page 6 of 6 Pages