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): May 25, 1999

                          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.)

     25 Science Park, New Haven, CT                                06511
----------------------------------------                         ----------
(Address of Principal Executive Offices)                         (Zip Code)

       Registrant's telephone number, including area code: (203) 776-1790

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

Item 5. Other Events

      On May 25, 1999, Alexion Pharmaceuticals, Inc. issued the press release
filed herewith as Exhibit 99.

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

      (c) Exhibits.

      99    Press Release dated May 25, 1999.
<PAGE>

                                   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, 1999             By:              /s/ Leonard Bell
                                  ----------------------------------------------
                                      Name:  Leonard Bell, M.D.
                                      Title: President, Chief Executive Officer,
                                             Secretary and Treasurer
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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): May 25, 1999

                          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.)

     25 Science Park, New Haven, CT                                06511
----------------------------------------                         ----------
(Address of Principal Executive Offices)                         (Zip Code)

       Registrant's telephone number, including area code: (203) 776-1790

                                 Not Applicable
                                 --------------
          (Former Name or Former Address, if Changed Since Last Report)
Item 5. Other Events

      On May 25, 1999, Alexion Pharmaceuticals, Inc. issued the press release
filed herewith as Exhibit 99.

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

      (c) Exhibits.

      99    Press Release dated May 25, 1999.
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, 1999             By:              /s/ Leonard Bell
                                  ----------------------------------------------
                                      Name:  Leonard Bell, M.D.
                                      Title: President, Chief Executive Officer,
                                             Secretary and Treasurer