EXHIBIT 32.a

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 OXIS International, Inc. (the “Company”) on Form 10-QSB for the period ending March 31, 2005 as filed with the Securities and Exchange Commission on the date therein specified (the “Report”), I, Steven. T. Guillen, Chief Executive Officer of the Company, certify pursuant to 18 U.S.C. Section 1350 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 result of operations of the Company at the dates and for the periods indicated.

This Certification has not been, and shall not be deemed, “filed” with the Securities and Exchange Commission.