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                                                                     EXHIBIT 5.1


                    [Fulbright & Jaworski L.L.P. Letterhead]



                               September 14, 2001

Alexion Pharmaceuticals, Inc.
352 Knotter Drive
Cheshire, CT 06410

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. (the "Company"), relating to 1,500,000 shares
of the Company's Common Stock, $0.0001 par value per share (the "Shares"), to be
issued under the Company's 2000 Stock Option Plan (the "Plan").

                  As counsel for the Company, we have examined such corporate
records, other documents, and such questions of law as we have considered
necessary or appropriate for the purposes of this opinion and, upon the basis of
such examination, advise you that in our opinion, all necessary corporate
proceedings by the Company have been duly taken to authorize the issuance of the
Shares pursuant to the Plan and that the Shares being registered pursuant to the
Registration Statement, when issued and paid for under the Plan in accordance
with the terms of the Plan, will be duly authorized, validly issued, fully paid
and non-assessable.

                  We hereby consent to the filing of this opinion as an exhibit
to the Registration Statement. This consent is not 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,


                                           /s/ Fulbright and Jaworski L.L.P.