Exhibit 5.1

Richard L. Edmonson

Vice President, General Counsel and Corporate Secretary

Syntroleum Corporation

16800 Greenspoint Park Drive, Suite 150S

Houston, Texas 77060

May 14, 2004

Syntroleum Corporation

4322 South 49th West Avenue

Tulsa, Oklahoma 74107

Ladies and Gentlemen:

As set forth in Amendment No. 1 to the Registration Statement on Form S-3 (Registration No. 333-111716) (the “Registration Statement”) to be filed on May 14, 2004 by Syntroleum Corporation, a Delaware corporation (the “Company”), with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), relating to the proposed sale from time to time, of (i) up to 3,645,000 shares (the “Offered Shares”) of common stock, par value $.01 per share, of the Company (the “Common Stock”), including 1,000,000 shares (the “Zilkha Warrant Shares”) of Common Stock issuable upon exercise of the Zilkha Warrants (as hereinafter defined), 1,170,000 shares (the “Ghandour Warrant Shares”) of Common Stock issuable upon exercise of the Ghandour Warrants (as hereinafter defined), 50,000 shares (the “Sovereign Warrant Shares” and, together with the Zilkha Warrant Shares and the Ghandour Warrant Shares, the “Warrant Shares”) of Common Stock issuable upon exercise of the Sovereign Warrants (as hereinafter defined) and 25,000 shares (the “Option Shares”) issuable pursuant to options (the “Options”) each for the purchase of one share of Common Stock, and (ii) up to 1,000,000 warrants each for the purchase of one share of Common Stock (the “Zilkha Warrants”), up to 1,170,000 warrants each for the purchase of one share of Common Stock (the “Ghandour Warrants”) and up to 50,000 warrants each for the purchase of one share of Common Stock (the “Sovereign Warrants” and, together with the Zilkha Warrants and the Ghandour Warrants, the “Warrants” and, together with the Offered Shares and the Option Shares, the “Securities”), certain legal matters in connection with the Securities are being passed upon for the Company by me. At your request, this opinion is being furnished to you for filing as Exhibit 5.1 to the Registration Statement.

The Zilkha Warrants are exercisable to acquire the Zilkha Warrant Shares pursuant to the terms and conditions set forth in the Warrant Agreement dated February 7, 2003 by and among the Company, Michael Zilkha and the Selim K. Zilkha Trust, which is filed as Exhibit 4.6 to the Registration Statement (the “Zilkha Warrant Agreement”), and the Zilkha Warrants, a form of which is filed as Exhibit 4.7 to the Registration Statement.

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The Ghandour Warrants are exercisable to acquire the Ghandour Warrant Shares pursuant to the terms and conditions set forth in the Warrant Agreement dated February 2, 2004 between the Company and Ziad Ghandour, which is filed as Exhibit 4.8 to the Registration Statement (the “Ghandour Warrant Agreement”), and the Ghandour Warrants, a form of which is included in Exhibit 4.8 to the Registration Statement.

The Sovereign Warrants are exercisable to acquire the Sovereign Warrant Shares pursuant to the terms and conditions set forth in the Warrant Agreement dated as of April 26, 2004 between the Company and Sovereign Oil & Gas Company II, LLC, which is filed as Exhibit 4.11 to the Registration Statement (the “Sovereign Warrant Agreement” and, together with the Zilkha Warrant Agreement and the Ghandour Warrant Agreement, the “Warrant Agreements”, and each, a “Warrant Agreement”), and the Sovereign Warrants, a form of which is included in Exhibit 4.11 to the Registration Statement.

The Options are exercisable to purchase the Option Shares pursuant to the terms and conditions set forth in the Director Stock Option Agreement, dated as of December 20, 2002, between the Company and James R. Seward, which is filed as Exhibit 4.9 to the Registration Statement (the “Option Agreement”).

In my capacity as General Counsel of the Company, I have examined the Company’s Certificate of Incorporation and Bylaws and the originals, or copies certified or otherwise identified, of corporate records of the Company, certificates of public officials and of representatives of the Company, statutes and other instruments and documents as a basis for the opinions hereinafter expressed. In giving such opinions, I have relied upon certificates of officers of the Company with respect to the accuracy of the material factual matters contained in such certificates.

I have assumed that all signatures on all documents examined by me are genuine, that all documents submitted to me as originals are accurate and complete, that all documents submitted to me as copies are true and correct copies of the originals thereof and that all information submitted to me was accurate and complete.

On the basis of the foregoing, and subject to the assumptions, limitations and qualifications hereinafter set forth, I am of the opinion that:

1. The Company is a corporation duly incorporated and validly existing in good standing under the laws of the State of Delaware.

2. The Securities (other than the Warrant Shares and the Option Shares) have been validly issued, fully paid and nonassessable.

3. The Warrants constitute legal, valid and binding obligations of the Company, entitled to the benefits of the applicable Warrant Agreement and will be enforceable against the Company in accordance with their terms, except as the enforceability thereof is subject to the effect of (A) any applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance or other law relating to or

Syntroleum Corporation -3- May 14, 2004

affecting creditors’ rights generally and (B) general principles of equity and public policy (regardless of whether such enforceability is considered in a proceeding in equity or at law).

4. If and when issued to holders of Warrants directly upon exercise thereof in accordance with all of the terms and conditions set forth in the Warrants, the Warrant Shares will be validly issued, fully paid and nonassessable.

5. If and when issued to holders of Options directly upon exercise thereof in accordance with all of the terms and conditions set forth in the Option Agreement, the Option Shares will be validly issued, fully paid and nonassessable.

I hereby consent to the filing of this opinion as an exhibit to the Registration Statement. I also consent to the reference to my name under the heading “Legal Matters” in the prospectus forming a part of the Registration Statement. In giving this consent, I do not hereby admit that I am in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ Richard L. Edmonson

Richard L. Edmonson

Vice President, General Counsel and Corporate Secretary