FILED PURSUANT TO RULE 424(b)(3)
                                                   REGISTRATION NUMBER 333-29493


                      SUPPLEMENT DATED DECEMBER 22, 1998
 
                        SUPPLEMENT NO. 1 TO PROSPECTUS
                            DATED DECEMBER 11, 1998
                                      OF
                         CORTEX PHARMACEUTICALS, INC.


Increase in Authorized Shares of Common Stock
- ---------------------------------------------

    On December 21, 1998, pursuant to approval by the Board of Directors and the
stockholders of Cortex Pharmaceuticals, Inc., a Delaware corporation (the
"Company"), the Company amended its Restated Certificate of Incorporation to
increase the number of authorized shares of common stock to 30,000,000 from
20,000,000. The sections of the Company's prospectus dated December 11, 1998
entitled "Capitalization" and "Description of Securities" are hereby
supplemented to reflect the foregoing information.