UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549


                                    FORM 8-K


                                 CURRENT REPORT


                       Pursuant to Section 13 or 15(d) of
                      The Securities Exchange Act of 1934


       Date of Report (Date of earliest event reported)     May 16, 1996
                                                            -------------


                          CORTEX PHARMACEUTICALS, INC.
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             (Exact name of registrant as specified in its charter)




              Delaware              0-17951             33-0303583
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    (State or other jurisdiction  (Commission         (IRS Employer
         of incorporation)        File Number)      Identification No)




           15241 Barranca Parkway, Irvine, California    92718
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          (Address of principal executive offices)     (Zip Code)




Registrant's telephone number, including area code (714) 727-3157




                                 Not Applicable
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         (Former name or former address, if changed since last report)

                           Page 1 of 12
                                            Exhibit Index on Page 4


ITEM 5.  OTHER EVENTS

    On May 16, 1996, Cortex Pharmaceuticals, Inc. (the "Company") announced
the appointment of Vincent F. Simmon, Ph.D., 52 as President and Chief
Executive Officer and member of the Board of Directors of the Company,
effective immediately.




ITEM 6.  EXHIBITS

    Exhibits:

       10.56  Employment Agreement dated May 15, 1996, between 
              Cortex Pharmaceuticals, Inc. and Vincent F. Simmon, Ph.D.

       21     Press Release dated May 16, 1996.





                           SIGNATURE

     Pursuant to the requirements of the Securities Exchange Act of 1934,
the registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.

                              CORTEX PHARMACEUTICALS, INC.



Date:  June 3, 1996           By: /s/ D. Scott Hagen
                                  ----------------------------------------------
                                      D. Scott Hagen
                                      Vice President and Chief Financial Officer



                         EXHIBIT INDEX


      Exhibits            Description
      --------            ----------- 

        10.56             Employment Agreement dated May 15, 1996, between
                          Cortex Pharmaceuticals, Inc. and Vincent F.
                          Simmon, Ph.D.

        21                Press release dated
                          May 16, 1996