Exhibit 5.1

Fulbright & Jaworski L.L.P.

A Registered Limited Liability Partnership

666 Fifth Avenue, 31st Floor

New York, New York 10103-3198

www.fulbright.com

telephone:	(212) 318-3000
facsimile:	(212) 318-3400

March 9, 2005

Alexion Pharmaceuticals, Inc.

352 Knotter Drive

Cheshire, Connecticut 06410

Re: Registration Statement on Form S-8

Ladies and Gentleman:

We refer to the Registration Statement on Form S-8 (the “Registration Statement”) to be filed with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Act”), on behalf of Alexion Pharmaceuticals, Inc., a Delaware corporation (the “Company”), relating to 3,093,519 shares of the Company’s Common Stock, $.0001 par value (the “Common Stock”), issuable pursuant to the Alexion Pharmaceuticals, Inc. 2004 Incentive Plan (the “Plan”).

As counsel to the Company, we have examined such corporate records, other documents and such questions of law as we have deemed necessary or appropriate for the purposes of this opinion and, upon the basis of such examinations, advise you that in our opinion the 3,093,519 shares of Common Stock issuable pursuant to the Plan have been duly and validly authorized and, subsequent to the exercise of the stock award and payment of the exercise price of the stock award, will be validly issued, fully paid and non-assessable.

We consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement. This consent is not to be construed as an admission that we are a person whose consent is required to be filed with the Registration Statement under the provisions of the Act.

Very truly yours,

Fulbright & Jaworski L.L.P.