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, 2013, 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. § 1350, as adopted pursuant to §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 9, 2013
	/s/ William A. Carter
	William A. Carter, M.D.
	Chief Executive Officer