EXHIBIT 5.1

                  [LETTERHEAD OF FULBRIGHT & JAWORSKI L.L.P]

April 27, 2001

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

Re:  Alexion Pharmaceuticals, Inc. Registration Statement on Form S-3
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Dear Sirs:

          In connection with the Registration Statement on Form S-3 (the
"Registration Statement") to be filed by Alexion Pharmaceuticals, Inc., a
Delaware corporation (the "Company"), under the Securities Act of 1933, as
amended, relating to the resale by certain stockholders of the Company of up to
an aggregate of 187,114 shares (the "Shares") of Common Stock, par value $.0001
per share, of the Company, we as counsel for the Company, have examined such
corporate records, other documents and questions of law as we have deemed
necessary or appropriate for the purposes of this opinion.

     Upon the basis of such examination, we advise you that in our opinion the
Shares have been duly and validly authorized, legally issued, fully paid and
non-assessable.

     We consent to the filing of this opinion as an exhibit to the Registration
Statement and to the reference to this firm under the caption "Legal Matters" in
the Prospectus contained therein and elsewhere in the Registration Statement and
Prospectus. This consent is not to be construed as an admission that we are a
party whose consent is required to be filed with the Registration Statement
under the provisions of the Securities Act of 1933, as amended.

                                    Very truly yours,

                                    /s/ Fulbright & Jaworski L.L.P.