EXHIBIT 32.1

                            CERTIFICATION PURSUANT TO
                               SECTION 906 OF THE
                           SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of Hemispherx Biopharma, Inc. (the
"Company") on Form 10-Q for the fiscal quarter ended June 30, 2006 as filed with
the Securities and Exchange Commission on the date hereof (the "Report"), I,
William A. Carter, Chief Executive Officer of the Company, certify, pursuant to
18 U.S.C. ss. 1350, as adopted pursuant to ss.906 of the Sarbanes-Oxley Act of
2002, that:

      (1) The Report fully complies with the requirements of section 13(a) or
15(d) of the Securities Exchange Act of 1934; and

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

Date: August 14, 2006


                                            /s/ William A. Carter
                                            ------------------------------------
                                            William A. Carter
                                            Chief Executive Officer