BioCryst Pharmaceuticals (BCRX) 10-K 2004 FY Annual report

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 Annual Report of BioCryst Pharmaceuticals, Inc. (the “Company”) on Form 10-K for the period ending December 31, 2004 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Charles E. Bugg, 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, to the best of my knowledge:

(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 results of operations of the Company.

/s/ CHARLES E. BUGG

Charles E. Bugg

Chief Executive Officer

March 14, 2005