Exhibit 99.1

For Immediate Release

OXIS RESEARCH ASSAY REVENUES GROW 37 PERCENT

IN THE FIRST QUARTER OF 2004

OXIS Reports First Quarter Financial Results

PORTLAND, Ore.—May 27, 2004 — OXIS International, Inc. (OTCBB:OXIS) (Nouveau Marche:OXIS) today announced financial results for the first quarter of 2004.

For the first quarter ended March 31, 2004, the Company reported revenues of $567,000, an increase in revenues over $549,000 reported in the first quarter of 2003. The net loss for the first quarter of 2004 was $593,000 compared to a net loss of $149,000 in the first quarter of 2003. The net loss during 2004 was primarily due to decreased fine chemical sales in the first quarter of 2004, increased professional fees associated with the Company’s January change of control by Axonyx Inc. (Nasdaq: AXYX), ongoing issues with the AMF in France, and financing fees and interest expense incurred for a convertible bridge loan. The Company’s Research Assay revenues grew to $524,000 in the first quarter of 2004, up from $383,000 in the first quarter of 2003.

The Company also announced the appointment of four new members to the OXIS Board of Directors: Dr. Gosse B. Bruinsma, President and Chief Operations Officer of Axonyx Europe; S. Colin Neill, Chief Financial Officer, Treasurer and Secretary of Axonyx Inc.; Dr. Gerard J. Vlak, Vice Chairman of the Board of Axonyx Inc. and Dr. Steven H. Ferris, Board Director of Axonyx Inc. These new appointments join Richard Davis, Dr. Timothy Rodell and Ray R. Rogers as directors of the Company.

“During the first quarter of 2004, OXIS incurred non-operational expenses related to the Axonyx transaction and a convertible bridge loan,” stated Ray R. Rogers, chairman and CEO of OXIS. “We are very pleased with the continued revenue growth of our research assays, as well as the progress we’ve made to expand our Animal Health Profiling Program, to further validate our Cardiac Predictor technologies and to commercialize the powerful antioxidant Ergothioneine as a nutritional supplement.”

In November 2003, the Company was notified that a Paris lower court (Tribunal de grande instance de Paris) issued an order requiring the Company to file its 2002 Reference Document as required under French law and the regulations of the Autorité des Marchés Financiers (AMF). OXIS has since filed its 2002 Reference Document, received confirmation from the

AMF that such document has been accepted and paid a settlement of approximately $11,600 relating to the order. However, pursuant to an AMF investigation concerning the Company’s failing to file financial and other disclosure information during 1999 through 2002 as required under French law, a hearing by the Disciplinary Commission of the AMF is scheduled for June 2004 to determine if a fine of not less than 100,000 Euros should be levied against the Company, as recommended by an AMF investigator. The Company intends to seek the elimination or reduction of the proposed fine at the hearing.

OXIS International Inc., headquartered in Portland, Oregon, focuses on developing technologies and products to research, diagnose, treat and prevent diseases associated with damage from free radical and reactive oxygen species – diseases of oxidative stress. The Company holds the rights to three therapeutic classes of compounds in the area of oxidative stress, and develops, manufactures and markets products and technologies to diagnose and treat diseases caused by oxidative stress.

Statements in this release that are not purely historical are forward-looking statements within the meaning of Section 27A of the Securities Act of 1933 and Section 21E of the Securities Exchange Act of 1934, including, without limitation, any statements regarding beliefs, plans, estimates, projections, expectations, goals or intentions regarding the future. Forward-looking statements in this release include statements regarding growth of the Company’s oxidative stress assays, the expansion of the Animal Health Profiling Program, validation of the Cardiac Predictor technologies, commercialization of the antioxidant Ergothioneine as a nutritional supplement, and the Company seeking the elimination or reduction of the proposed fines at the upcoming AMF hearing. Factors that could cause actual results to differ materially from the forward-looking statements include risks and uncertainties such as the Company’s ability to raise adequate funding, unforeseen difficulties related to the Company’s oxidative stress and other diagnostic products; decreases in the rate of spending by the Company’s customers; the development by the Company’s competitors of new competing products; and other risks indicated in the Company’s filings with the Securities and Exchange Commission. It is important to note that actual outcomes could differ materially from those in such forward-looking statements. Readers should also refer to the documents filed by the Company with the Securities and Exchange Commission, specifically the annual report on Form 10-KSB for the year ended December 31, 2003, filed with the Securities and Exchange Commission on March 26, 2004 and the Company’s quarterly reports on Form 10-QSB filed thereafter.

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OXIS INTERNATIONAL, INC. AND SUBSIDIARIES

CONSOLIDATED STATEMENTS OF OPERATIONS

(In thousands of dollars, except earnings per share data)

CONSOLIDATED BALANCE SHEET INFORMATION

(In thousands of dollars)

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