EXHIBIT 32.1

CERTIFICATION PURSUANT TO
18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO
SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

     In connection with the Quarterly Report of Advanced Viral Research Corp. (the “Company”) on Form 10-Q for the period ending March 31, 2004 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), we, the undersigned, certify, pursuant to 18 U.S.C. Section 1350, as Adopted Pursuant to Section 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, as amended; and

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

Date: May 14, 2004

/s/ Elma S. Hawkins PhD, MBA

Elma S. Hawkins, PhD, MBA
President and Chief Executive Officer