EXHIBIT 32

                    CERTIFICATION OF CHIEF EXECUTIVE OFFICER

Pursuant to 18 U.S.C. 1350, as created by Section 906 of the Sarbanes-Oxley Act
of 2002, the undersigned officer of CytRx Corporation (the "Company") hereby
certifies that:

(i) the accompanying Quarterly Report on Form 10-Q of the Company for the three
months ended March 31, 2004 (the "Report") fully complies with the requirements
of Section 13(a) or Section 15(d), as applicable, of the Securities Exchange Act
of 1934, as amended; and

(ii) the information contained in the Report fairly presents, in all material
respects, the financial condition and results of operations of the Company.

Date: May 17, 2004                       /s/  STEVEN A. KRIEGSMAN
                                         ------------------------
                                         Steven A. Kriegsman
                                         Chief Executive Officer


A signed original of this written statement required by Section 906 of the
Sarbanes-Oxley Act of 2002 (Section 906), or other document authenticating,
acknowledging, or otherwise adopting the signature that appears in typed form
within the electronic version of this written statement required by Section 906,
has been provided to CytRx Corporation and will be retained by CytRx Corporation
and furnished to the Securities and Exchange Commission or its staff upon
request.

                   CERTIFICATION OF CHIEF FINANCIAL OFFICER

Pursuant to 18 U.S.C. 1350, as created by Section 906 of the Sarbanes-Oxley Act
of 2002, the undersigned officer of CytRx Corporation (the "Company") hereby
certifies that:

(i) the accompanying Quarterly Report on Form 10-Q of the Company for the three
months ended March 31, 2004 (the "Report") fully complies with the requirements
of Section 13(a) or Section 15(d), as applicable, of the Securities Exchange Act
of 1934, as amended; and

(ii) the information contained in the Report fairly presents, in all material
respects, the financial condition and results of operations of the Company.

Date: May 17, 2004                       /s/  C. KIRK PEACOCK
                                         --------------------
                                         C. Kirk Peacock
                                         Chief Financial Officer

A signed original of this written statement required by Section 906 of the
Sarbanes-Oxley Act of 2002 (Section 906), or other document authenticating,
acknowledging, or otherwise adopting the signature that appears in typed form
within the electronic version of this written statement required by Section 906,
has been provided to CytRx Corporation and will be retained by CytRx Corporation
and furnished to the Securities and Exchange Commission or its staff upon
request.