PROSPECTUS SUPPLEMENT NO. 1
(TO PROSPECTUS DATED JANUARY 9, 1998)

                                                               FILED PURSUANT TO
                                                                  RULE 424(B)(3)
                                                            FILE NOS.: 333-44043
                                                                   AND 333-39607
                                                                                
                                 233,864 Shares

                               CYTRX CORPORATION

                                  COMMON STOCK

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     This Prospectus Supplement relates to the offering for resale from time to
time (the "Offering") by the holders of 233,864 shares (the "Shares") of Common
Stock, $0.001 par value (the "Common Stock"), of CytRx Corporation, a Delaware
corporation ("CytRx" or the "Company").

     This Prospectus Supplement is not complete without, and may not be
delivered or utilized except together with, the Prospectus dated January 9,
1998.  All capitalized terms used but not defined in this Prospectus Supplement
shall have the meanings given them in the Prospectus.

     The line item "Charles N. Eckert .............. 9,673(5)" contained in the
table set forth in the Prospectus under the caption "Selling Stockholders" is
hereby deleted in its entirety and replaced with "Charles N. Eckert
 .............. 11,124(5)."

     The footnote "(5)  Represents 500 Shares from which Warrants held by
Charles N. Eckert are exercisable and 9,173 Shares that the Company expects to
be issued upon conversion of all of the Debentures held by Charles N. Eckert
using a Conversion Price of $2.7253." contained in the Prospectus under the
caption "Selling Stockholders" is hereby deleted in its entirety and replaced
with "(5) Includes 500 Shares for which Warrants held by Charles N. Eckert are
exercisable and 10,624 Shares that the Company issued in March 1998 upon
conversion of $50,000 of Debentures held by Mr. Eckert at a Conversion Price of
$2.385."

     THE SECURITIES OFFERED HEREBY INVOLVE A HIGH DEGREE OF RISK.  SEE "RISK
FACTORS" BEGINNING ON PAGE 6 OF THE PROSPECTUS FOR INFORMATION THAT SHOULD BE
CONSIDERED BY PROSPECTIVE PURCHASERS.

 
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         THESE SECURITIES HAVE NOT BEEN APPROVED OR DISAPPROVED BY THE
           SECURITIES AND EXCHANGE COMMISSION OR ANY STATE SECURITIES
           COMMISSION NOR HAS THE COMMISSION OR ANY STATE SECURITIES
               COMMISSION PASSED UPON THE ACCURACY OR ADEQUACY OF
                  THIS PROSPECTUS.  ANY REPRESENTATION TO THE
                        CONTRARY IS A CRIMINAL OFFENSE.

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

           The date of this Prospectus Supplement is August 20, 1998.