UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 8-K

CURRENT REPORT

Pursuant to Section 13 or 15(d) of

the Securities Exchange Act of 1934

Date of Report (Date of earliest event reported): May 21, 2004

SYNTROLEUM CORPORATION

(Exact name of registrant as specified in its charter)

Delaware	0-21911	73-1565725
(State or other jurisdiction of incorporation)	(Commission File Number)	(IRS Employer Identification No.)

4322 South 49th West Avenue
Tulsa, Oklahoma	74107
(Address of principal executive offices)	(Zip Code)

Registrant’s telephone number, including area code: (918) 592-7900

ITEM 5. OTHER EVENTS.

On May 21, 2004, Syntroleum Corporation, a Delaware corporation (the “Company”), entered into an Underwriting Agreement dated May 21, 2004 (the “Underwriting Agreement”) between the Company and Jefferies & Company, Inc. The Underwriting Agreement related to an offering of 5,916,000 shares of the Company’s common stock, par value $0.01 per share (the “Common Stock”), and 887,400 warrants (the “Warrants”) to purchase initially 887,400 shares of Common Stock under a registration statement on Form S-3 (Registration No. 333-62290) (the “Registration Statement”). The Company expects to enter into a Warrant Agreement between the Company and American Stock Transfer and Trust Company, as warrant agent (the “Warrant Agent”), setting forth certain terms of the Warrants and including as an exhibit a form of Warrant. This Current Report on Form 8-K is being filed for the purpose of filing as exhibits the Underwriting Agreement, a form of the Warrant Agreement, the form of Warrant, an opinion of Baker Botts L.L.P. and a consent of Grant Thornton LLP, in connection with the Registration Statement and the offering of Common Stock and Warrants.

ITEM 7. FINANCIAL STATEMENTS AND EXHIBITS.

The following exhibits are filed herewith:

1.1	Underwriting Agreement dated May 21, 2004 between the Company and Jefferies & Company, Inc.
4.1	Form of Warrant Agreement to be dated as of May 26, 2004 between the Company and the Warrant Agent
4.2	Form of Warrant (contained in Exhibit 4.1)
5.1	Opinion of Baker Botts L.L.P.
23.1	Consent of Baker Botts L.L.P. (included in Exhibit 5.1)
23.2	Consent of Grant Thornton LLP

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SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.

		SYNTROLEUM CORPORATION
Date:	May 24, 2004	By:	/s/    RICHARD L. EDMONSON
			Richard L. Edmonson            Vice President, General Counsel            and Corporate Secretary

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EXHIBIT INDEX

EXHIBIT NUMBER	EXHIBIT DESCRIPTION
1.1	Underwriting Agreement dated May 21, 2004 between the Company and Jefferies & Company, Inc.
4.1	Form of Warrant Agreement to be dated as of May 26, 2004 between the Company and the Warrant Agent
4.2	Form of Warrant (contained in Exhibit 4.1)
5.1	Opinion of Baker Botts L.L.P.
23.1	Consent of Baker Botts L.L.P. (included in Exhibit 5.1)
23.2	Consent of Grant Thornton LLP

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