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


                                APRIL 30, 2001
                       ---------------------------------
                       (Date of earliest event reported)


                         CORTEX PHARMACEUTICALS, INC.
              --------------------------------------------------
              (Exact name of Registrant as specified in charter)


          DELAWARE                  0-17951                 33-0303583
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(State or other jurisdiction      (Commission           (I.R.S. Employer
       of incorporation)          File Number)          Identification No.)


15241 BARRANCA PARKWAY
IRVINE, CALIFORNIA                                            92618
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(Address of principal executive offices)                    (Zip Code)


                                (949) 727-3157
             ----------------------------------------------------
             (Registrant's telephone number, including area code)


                                NOT APPLICABLE
        ---------------------------------------------------------------
        (Former name or former address, if changed, since last report.)


                               Page 1 of 2 Pages
                            Exhibit Index on Page 2


ITEM 5.   OTHER EVENTS.

          On April 30, 2001, Cortex Pharmaceuticals, Inc. announced that it was
approved for trading on the American Stock Exchange. It will trade under the
symbol COR.

          The press release is being filed herewith as Exhibit 99.1 to this
Current Report. The Exhibit is incorporated herein by reference.



        EXHIBIT
        NUMBER         DESCRIPTION
        -------        -----------

        99.1           Press Release dated April 30, 2001.




                                  SIGNATURES

          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 hereunto duly authorized.

Date: MAY 2, 2001                      CORTEX PHARMACEUTICALS, INC.

                                       /s/ MARIA S. MESSINGER
                                       -------------------------------------
                                       Maria S. Messinger
                                       Vice President, Chief Financial Officer
                                       and Corporate Secretary
                                       (Chief Accounting Officer)



                                 EXHIBIT INDEX



EXHIBIT NUMBER      DESCRIPTION                                      PAGE NUMBER
--------------      -----------                                      -----------

     99.1           Press Release dated April 30, 2001.

                                       2