Exhibit 99.1

EXECUTION COPY

OXIS INTERNATIONAL, INC.

CONVERSION AGREEMENT

THIS CONVERSION AGREEMENT (this “Agreement”) is entered into as of May 23, 2005 by and between OXIS International, Inc., a Delaware corporation (the “Company”), and Equitis Entreprise, a French société par actions simplifiée (“Equitis”).

R E C I T A L S

WHEREAS, the Company issued a promissory note dated April 9, 1997 in the principal amount of U.S. $160,000.00 and yielding an interest rate of eight percent (8%) per annum (the “Note”), to Finovelec, a French société anonyme (“Finovelec”);

WHEREAS, Finovelec transferred the Note to Equitis, which at the time of such transfer was named Infinitis;

WHEREAS, as of the date hereof, the total principal, accrued interest and origination fee owed to Equitis by the Company pursuant to the Note is U.S. $243, 458.63 (the “Amount Owed”); and

WHEREAS, Equitis desires to convert the Amount Owed into shares of the Company’s Common Stock and terminate the Note on the terms set forth herein;

NOW, THEREFORE, in consideration of the mutual promises and covenants hereinafter set forth, the parties to this Agreement hereby agree as follows:

A G R E E M E N T

1. Conversion of the Note and Issuance of Company Common Stock.

(a) Contemporaneously with the execution of this Agreement, Equitis shall terminate the Note and convert the Amount Owed at a conversion price of $0.53 (the “Conversion Price”), in consideration for the Company selling and issuing to Equitis four hundred fifty nine thousand three hundred fifty-five (459,355) shares of the Company’s Common Stock (the “Conversion Shares”), which number equals the Amount Owed divided by the Conversion Price (without regard to fractional shares).

(b) Contemporaneously with the execution of this Agreement, the Company shall sell and issue the Conversion Shares to Equitis in consideration for Equitis terminating the Note and converting the Amount Owed into the Conversion Shares. A certificate representing the Conversion Shares shall be delivered by the Company as soon as reasonably practicable.

1

2. General Release; Termination of the Note.

(a) As further consideration for the Company’s sale and issuance to Equitis of the Conversion Shares, Equitis hereby releases and forever discharges the Company, its affiliated, related, parent or subsidiary entities, and each of their past, present and future stockholders, directors, officers, agents, employees, partners, representatives, attorneys, accountants, and all persons acting by, through, under or in concert with any of them (the “Released Parties”) from any and all claims, actions, causes of action, suits, debts, liens, demands, contracts, liabilities, agreements, costs, expenses, or losses of any type, whether known or unknown, fixed or contingent, which Equitis had or may now have, that relate to or arise from any act or omission or condition that occurred on or prior to the date of this Agreement, including, but not limited to, any and all claims arising from or relating to the Note, whether based on contract, tort, statute, regulation or any comparable law in any jurisdiction (the “Released Claims”). Equitis also agrees not to initiate or cause to be initiated against any of the Released Parties any lawsuit, investigation or proceeding of any kind which pertain in any manner to the Released Claims, or participate in the same, individually or as a member of a class.

3. Investment Representations.

(a) This Agreement is made in reliance upon Equitis’s representation to the Company, which by its acceptance hereof Equitis hereby confirms, that the Conversion Shares to be received by Equitis will be acquired for investment for its own account, not as a nominee or agent, and not with a view to the sale or distribution of any part thereof, and that Equitis has no present intention of selling, granting participation in, or otherwise distributing the same, but subject nevertheless to any requirement of law that the disposition of Equitis’s property shall at all times be within its control. Equitis also represents and warrants that it has sufficient business and financial experience to enable it to protect its own interests in connection with the purchase of the Conversion Shares hereunder.

(b) Equitis believes that it has received all the information it considers necessary or appropriate for deciding whether to purchase the Conversion Shares. Equitis further represents that it has had an opportunity to ask questions and receive answers from the Company regarding the business, properties, prospects and financial condition of the Company.

(c) Equitis is an “accredited investor” within the meaning of Securities and Exchange Commission (“SEC”) Rule 501 of Regulation D, as presently in effect.

(d) Equitis understands that the Conversion Shares it is purchasing are characterized as “restricted securities” under the federal securities laws inasmuch as they are being acquired from the Company in a transaction not involving a public offering and that under such laws and applicable regulations such securities may be resold without registration under the Securities Act of 1933, as amended (the “Act”) only in certain limited circumstances. In this connection, Equitis represents that it is familiar with SEC Rule 144, as presently in effect, and understands the resale limitations imposed thereby and by the Act. Equitis understands that the Conversion Shares have not been and will not be registered under the Act and have not been and will not be registered or qualified in any state in which they are offered, and thus Equitis will not be able to resell or otherwise transfer the Conversion Shares unless they are registered under the Act and registered or qualified under applicable state securities laws, or an exemption from such registration or qualification is available.

2

4. Legends. It is understood that the certificate(s) evidencing the Conversion Shares shall bear the following legend:

“THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED. THEY MAY NOT BE SOLD, OFFERED FOR SALE, PLEDGED OR HYPOTHECATED IN THE ABSENCE OF A REGISTRATION STATEMENT IN EFFECT WITH RESPECT TO THE SECURITIES UNDER SUCH ACT OR AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED OR UNLESS SOLD PURSUANT TO RULE 144 OF SUCH ACT.”

5. Cancellation of the Note. As a condition precedent to the effectiveness of this Agreement, Equitis shall deliver an original copy of the Note to the Company and hereby authorizes and directs the Company to mark the Note cancelled and paid in full.

6. Termination of the Note. The parties hereby agree that the Note is hereby terminated and has no further force or effect, and Equitis hereby waives the survival of any part thereof.

7. Oregon Law. This Agreement is to be construed in accordance with and governed by the internal laws of the State of Oregon without giving effect to any choice of law rule that would cause the application of the laws of any jurisdiction other than the internal laws of the State of Oregon.

8. Notice. Any notice required to be given under the terms of this Agreement shall be addressed to the Company in care of its Secretary at the office of the Company at 6040 N. Cutter Circle, Suite 317, Portland, Oregon 97217-3935, and any notice to be given to Equitis shall be addressed to it at the address given by Equitis beneath its signature to this Agreement, or such other address as either party to this Agreement may hereafter designate in writing to the other. Any such notice shall be deemed to have been duly given when enclosed in a properly sealed envelope or wrapper addressed as aforesaid, registered or certified and deposited (postage or registration or certification fee prepaid) in a post office or branch post office regularly maintained by the United States.

9. Successors and Assigns. Except as otherwise provided herein, the terms and conditions of this Agreement shall inure to the benefit of and be binding upon the respective successors and assigns of the parties. Nothing in this Agreement, express or implied, is intended to confer upon any party other than the parties hereto or their respective successors and assigns any rights, remedies, obligations, or liabilities under or by reason of this Agreement, except as expressly provided in this Agreement.

10. Counterparts. This Agreement may be executed in two or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

[Signature Page Follows]

3

IN WITNESS WHEREOF, the parties hereto have duly executed this Conversion Agreement as of the date first above written.