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. __)*

                                   Axonyx Inc.
-------------------------------------------------------------------------------
                                (Name of Issuer)


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


                                    05461R101
                      -------------------------------------
                                 (CUSIP Number)


                                December 21, 2005
                      -------------------------------------
                          (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)

                                   Page 1 of 5

                    ----------------------------------------


* 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).


                                  SCHEDULE 13G

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CUSIP No. 05461R101                                            Page 2 of 5 Pages
-------------------------------------       ------------------------------------

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  1    NAME OF REPORTING PERSON
       S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

       Lloyd I. Miller, III                      279-42-7925
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  2    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*               (a)   |_|

                                                                       (b)   |_|
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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

      NUMBER OF                  2,140,057
       SHARES                  -------------------------------------------------
    BENEFICIALLY               6 SHARED VOTING POWER
      OWNED BY
        EACH                     995,000
      REPORTING                -------------------------------------------------
       PERSON                  7 SOLE DISPOSITIVE POWER
        WITH
                                 2,140,057
                               -------------------------------------------------
                               8 SHARED DISPOSITIVE POWER

                                 995,000
--------------------------------------------------------------------------------
  9    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

       3,135,057
--------------------------------------------------------------------------------
  10   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN
       SHARES*                                                               |_|
--------------------------------------------------------------------------------
11     PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

       5.8%
--------------------------------------------------------------------------------
  12   TYPE OF REPORTING PERSON

       IN-IA-OO**
--------------------------------------------------------------------------------
                 *SEE INSTRUCTIONS BEFORE FILLING OUT!

** See Item 4.


                                                                     Page 3 of 5


Item 1(a). Name of Issuer:                      Axonyx Inc.

Item 1(b). Address of Issuers's Principal       500 Seventh Avenue, 10th Floor
           Executive Offices:                   New York, New York  10018

Item 2(a). Name of Person Filing:               Lloyd I. Miller, III

Item 2(b). Address of Principal Business        4550 Gordon Drive, Naples,
           Office or, if None, Residence:       Florida 34102

Item 2(c). Citizenship:                         U.S.A.

Item 2(d). Title of Class of Securities:        Common Stock

Item 2(e). CUSIP Number:                        05461R101

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:

           Not Applicable, this statement is filed pursuant to 13d-1(c)

Item 4.    OWNERSHIP: The reporting person has sole voting and dispositive
           power with respect to 2,140,057 of the reported securities as (i) the
           manager of a limited liability company that is the general partner of
           a certain limited partnership, (ii) as the custodian to accounts set
           up under the Florida Uniform Gift to Minors Act and (iii) as an
           individual. The reporting person has shared voting and dispositive
           power with respect to 995,000 of the reported securities as an
           investment advisor to the trustee of a certain family trust.

           (a) 3,135,057

           (b) 5.8%

           (c) (i) sole voting power:   2,140,057

               (ii) shared voting power: 995,000

               (iii) sole dispositive power: 2,140,057

               (iv) shared dispositive power: 995,000

Item 5.    OWNERSHIP OF FIVE PERCENT OR LESS OF A CLASS:

           Not Applicable

Item 6.    OWNERSHIP  OF MORE THAN  FIVE  PERCENT  ON  BEHALF OF  ANOTHER
           PERSON:

           Other than shares held directly by Lloyd I. Miller, III, persons
           other than Lloyd I. Miller III, have the right to receive or the
           power to direct the receipt of dividends from, or the proceeds from
           the sale of, the reported securities.

Item 7.    IDENTIFICATION AND CLASSIFICATION OF THE SUBSIDIARY WHICH ACQUIRED
           THE SECURITY BEING REPORTED ON BY THE PARENT HOLDING COMPANY:

           Not Applicable


                                                                     Page 4 or 5


Item 8.    IDENTIFICATION AND CLASSIFICATION OF MEMBERS OF THE GROUP:

           Not Applicable

Item 9.    NOTICE OF DISSOLUTION OF GROUP:

           Not Applicable

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.


                                                                     Page 5 of 5

                                    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.


      Dated: December 29, 2005                  /s/ Lloyd I. Miller, III
                                                --------------------------------
                                                Lloyd I. Miller, III