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) June 7, 2001
                                                           ------------


                          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 June 7, 2001, Alexion Pharmaceuticals, Inc. issued the press releases
filed herewith as Exhibit 99.1 and Exhibit 99.2.



ITEM 7. FINANCIAL STATEMENTS, PRO FORMA FINANCIAL INFORMATION AND EXHIBITS.

      (C)  EXHIBITS.

      99.1  Press Release dated June 7, 2001.

      99.2  Press Release dated June 7, 2001.








                                   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: June 7, 2001                  By:    /s/ LEONARD BELL, M.D.
                                       -----------------------------------------
                                    Name:  Leonard Bell, M.D.
                                    Title: President, Chief Executive Officer,
                                           Secretary and Treasurer



EXHIBIT INDEX

      99.1  Press Release dated June 7, 2001.

      99.2  Press Release dated June 7, 2001