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) September 12, 2003



                          ALEXION PHARMACEUTICALS, INC.
--------------------------------------------------------------------------------
             (Exact Name of Registrant as Specified in its Charter)



                                                                             
Delaware                                        0-27756            13-3648318
-------------------------------------------   ------------   -------------------
(State or Other Jurisdiction                  (Commission    (IRS Employer
of Incorporation)                             File Number)   Identification No.)


352 Knotter Drive, Cheshire, CT                                   06410
-------------------------------                                   ------
(Address of Principal Executive Offices)                        (Zip Code)




Registrant's telephone number, including area code:       (203) 272-2596
                                                     -------------------


                                 Not Applicable
--------------------------------------------------------------------------------
          (Former Name or Former Address, if Changed Since Last Report)




Item 5.  Other Events

         On September 12, 2003, the Company entered into an agreement to sell an
aggregate of 3,600,000 shares of its common stock, $.0001 par value per share,
to a syndicate led by Bear, Stearns & Co. Inc. The sale is made under the
Company's shelf-registration statement (Registration No. 333-47594 filed October
6, 2000) relating to the possible sale from time to time of the Company's
securities. This Form 8-K is filed to incorporate the exhibit hereto into that
registration statement.

Item 7.  Financial Statements, Pro Forma Financial Information and Exhibits.

         (c)  Exhibits.

         5.1      Opinion of Fulbright & Jaworski L.L.P.

                                       2



                                   SIGNATURES

         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.

                                            ALEXION PHARMACEUTICALS, INC.

Date: September 16, 2003                    By: /s/ David Keiser
                                                ----------------
                                            Name: David Keiser

                                            Title: President



                                        3