RULE 424(b)(3)
                                                      REGISTRATION NO. 333-29493

 
                      SUPPLEMENT DATED DECEMBER 23, 1998
 
                        SUPPLEMENT NO. 2 TO PROSPECTUS
                            DATED DECEMBER 11, 1998
                                      OF
                         CORTEX PHARMACEUTICALS, INC.



Increase in Number of Shares of Common Stock Issuable Upon Conversion of Series
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A Preferred Stock
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  As of December 23, 1998 the effective conversion price for the Company's
Series A Preferred Stock has decreased from $0.5379 per share to $0.3481 per
share due to a reduction in the market price of the Company's common stock.
Since December 11, 1998, the Company has issued 329,064 of the 525,556 shares of
common stock included in the prospectus as issuable upon conversion of the
Series A Preferred Stock.  As of December 23, 1998, at an effective conversion
price of $0.3481 per share, the number of shares of common stock issuable upon
conversion of the outstanding Series A Preferred Stock is 406,927.  The
prospectus cover page and the outside back cover page of the Company's
prospectus dated December 11, 1998 and the table entitled "Selling Stockholders"
are hereby supplemented to reflect the foregoing information.