<PAGE>


                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                 AMENDMENT NO. 3
                                       TO
                                  SCHEDULE 13D
                    UNDER THE SECURITIES EXCHANGE ACT OF 1934


                          ALEXION PHARMACEUTICALS, INC.
- --------------------------------------------------------------------------------
                                (Name of Issuer)

                         COMMON STOCK, $.0001 PAR VALUE
- --------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                    015351109
                                  ------------
                                 (CUSIP Number)

                                 Mark H. Swartz
                            Executive Vice President
                        c/o Tyco International (US) Inc.
                                  One Tyco Park
                                Exeter, NH 03833
                                 (603) 778-9700

                                Michael W. Lyons
                                Corporate Counsel
                       United States Surgical Corporation
                                150 Glover Avenue
                           Norwalk, Connecticut 06856
                                 (203) 845-1000

                                 with a copy to:

                            Frederick W. Kanner, Esq.
                              Dewey Ballantine LLP
                           1301 Avenue of the Americas
                          New York, New York 10019-6092
                                 (212) 259-8000


- --------------------------------------------------------------------------------
 (Name, Address and Telephone Number of Person Authorized to Receive Notices
                             and Communications)


                                DECEMBER 30, 1998
- --------------------------------------------------------------------------------
             (Date of Event which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report
the acquisition which is the subject of this Schedule 13D, and is filing this
schedule because of Sections 240.13d-1(e), 240.13d-1(f) or 240.13d-1(g), check
the following box / /.

NOTE: Schedules filed in paper format shall include a signed original and five
copies of the schedule, including all exhibits. See Rule 13d-7 for other parties
to whom copies are to be sent.


                        (Continued on following pages)
                             (Page 1 of 7 Pages)


<PAGE>


                                 SCHEDULE 13D


<TABLE>
<CAPTION>

- -------------------------------------            --------------------------------------------
CUSIP NO. 015351109                              PAGE    2     OF     7      PAGES
         ---------------------------                  -------      -------      
- -------------------------------------            --------------------------------------------

- ---------------------------------------------------------------------------------------------
<S>     <C>                                                                      <C>
   1

          NAME OF REPORTING PERSON:  Tyco International Ltd.


          S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON:

                            Not Applicable
- ---------------------------------------------------------------------------------------------
   2
          CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                       (a) /X/
                                                                                  (b) / /

- ---------------------------------------------------------------------------------------------
   3
          SEC USE ONLY


- ---------------------------------------------------------------------------------------------
   4
          SOURCE OF FUNDS*

                            Not Applicable
- ---------------------------------------------------------------------------------------------
   5
          CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO ITEMS 2(d)
          or 2(e)                                                                     / /


- ---------------------------------------------------------------------------------------------
   6
          CITIZENSHIP OR PLACE OF ORGANIZATION

                Bermuda
- ---------------------------------------------------------------------------------------------
                       7
                           SOLE VOTING POWER
  NUMBER OF SHARES
    BENEFICIALLY                 Not Applicable
      OWNED BY
        EACH
     REPORTING
       PERSON
        WITH
                     ------------------------------------------------------------------------
                       8
                           SHARED VOTING POWER

                                 Not Applicable

                     ------------------------------------------------------------------------
                       9
                           SOLE DISPOSITIVE POWER

                                 Not Applicable

                     ------------------------------------------------------------------------
                      10
                           SHARED DISPOSITIVE POWER

                                 Not Applicable
- ---------------------------------------------------------------------------------------------
  11
          AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                0
- ---------------------------------------------------------------------------------------------
  12
          CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*      / /

                Not Applicable
- ---------------------------------------------------------------------------------------------
  13
          PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

          0%
- ---------------------------------------------------------------------------------------------
  14
          TYPE OF REPORTING PERSON*

                CO
- ---------------------------------------------------------------------------------------------
</TABLE>


                    *SEE INSTRUCTIONS BEFORE FILLING OUT!
             INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
         (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION


<PAGE>

                                  SCHEDULE 13D


<TABLE>
<CAPTION>
- ------------------------------------                     ----------------------------------
CUSIP NO. 015351109                                      PAGE    3      OF      7
          -----------------------                             -------        ------- PAGES
- ------------------------------------                     ----------------------------------

- -------------------------------------------------------------------------------------------
<S>     <C>                                                                      <C>
   1
        NAME OF REPORTING PERSON:  United States Surgical Corporation


        S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON:

                          132518270
- -------------------------------------------------------------------------------------------
   2
        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                         (a) /X/
                                                                                  (b) / /

- -------------------------------------------------------------------------------------------
   3
        SEC USE ONLY


- -------------------------------------------------------------------------------------------
   4
        SOURCE OF FUNDS*

                          Not Applicable
- -------------------------------------------------------------------------------------------
   5
        CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO ITEMS 2(d)
        or 2(e)                                                                       / /


- -------------------------------------------------------------------------------------------
   6
        CITIZENSHIP OR PLACE OF ORGANIZATION

              Delaware
- -------------------------------------------------------------------------------------------
                   7
                      SOLE VOTING POWER
   NUMBER OF
     SHARES                 Not Applicable
  BENEFICIALLY
    OWNED BY
      EACH
   REPORTING
     PERSON
      WITH
                 --------------------------------------------------------------------------
                   8
                      SHARED VOTING POWER

                            Not Applicable

                 --------------------------------------------------------------------------
                   9
                      SOLE DISPOSITIVE POWER

                            Not Applicable

                 --------------------------------------------------------------------------
                  10
                      SHARED DISPOSITIVE POWER

                            Not Applicable
- -------------------------------------------------------------------------------------------
  11
        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

              0
- -------------------------------------------------------------------------------------------
  12
        CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*         / /

              Not Applicable
- -------------------------------------------------------------------------------------------
  13
        PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

        0%
- -------------------------------------------------------------------------------------------
  14
        TYPE OF REPORTING PERSON*

              CO
- -------------------------------------------------------------------------------------------
</TABLE>


                    *SEE INSTRUCTIONS BEFORE FILLING OUT!
             INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
         (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION



<PAGE>

            Tyco International Ltd., a Bermuda company ("Tyco") and United
States Surgical Corporation, a Delaware corporation and an indirect wholly owned
subsidiary of Tyco ("US Surgical") hereby further amend and supplement Statement
on 13D previously filed by Tyco and US Surgical (the "Schedule 13D") relating to
the common stock $.0001 par value (the "Common Stock"), of Alexion
Pharmaceuticals, Inc., a Delaware corporation (the "Issuer"), originally filed
with the Securities and Exchange Commission (the "Commission") on February 29,
1996, as amended. The item numbers and responses thereto below are in accordance
with the requirements of Schedule 13D.

            Unless otherwise indicated herein, each capitalized term used but
not defined herein shall have the meaning assigned to such term in the
Schedule 13D. The term Reporting Persons means Tyco and US Surgical.

            The Schedule 13D is hereby amended as follows:


ITEM 5.  INTEREST IN SECURITIES OF THE ISSUER.

            (a)   Number of Shares Beneficially Owned:

                  As of the date hereof, the Reporting Persons own an aggregate
                  of 0 shares of Common Stock of the Issuer.

            (b)   Sole Power to Vote, Direct the Vote of, Dispose of, or Direct
                  the Disposition of Shares:

                  Not Applicable.

            (c)   Recent Transactions:

                  On December 30, 1998, the Reporting Persons sold 824,087
                  shares of Common Stock of the Issuer in open market
                  transactions at a price of $11.625 per share.

            (d)   Rights with Respect to Dividends on Sales Proceeds:

                  Not Applicable.

            (e)   Date of  Cessation  of Five  Percent  Beneficial  Ownership:
                  12/30/98.


                              (Page 4 of 7 Pages)


<PAGE>


ITEM 7.  MATERIAL TO BE FILED AS EXHIBITS.

            Item 7 of the Schedule 13D is hereby amended and supplemented by the
following:


<TABLE>
<CAPTION>

EXHIBIT NO.                                 DESCRIPTION
- -----------                                 -----------
<S>                   <C>
1                         Agreement of Joint Filing pursuant to Rule 13d-1(k)(1)
                          promulgated under the Securities Exchange Act of 1934,
                          as amended.
</TABLE>



                              (Page 5 of 7 Pages)


<PAGE>

            After reasonable inquiry and to the best knowledge and belief of the
undersigned, the undersigned certifies that the information set forth in this
statement is true, complete and correct.


Date: January 21, 1999


                              TYCO INTERNATIONAL LTD.

                              By:        /s/ MARK H. SWARTZ      
                                 -----------------------------------------
                                 Name: Mark H. Swartz
                                 Title:Executive Vice President, Chief
                                       Financial Officer


                              UNITED STATES SURGICAL CORPORATION

                              By:        /s/ MARK H. SWARTZ      
                                 -----------------------------------------
                                 Name: Mark H. Swartz
                                 Title:   Vice President


                              (Page 6 of 7 Pages)







<PAGE>


                                                                       Exhibit 1


                          Agreement of Joint Filing

            Pursuant to 13d-1(k)(1) promulgated under the Securities Exchange
Act of 1934, as amended, the undersigned persons hereby agree to file with the
Securities and Exchange Commission the Statement on Schedule 13D (the
"Statement") to which this Agreement is attached as an exhibit, and agree that
such Statement, as so filed, is filed on behalf of each of them.

            IN WITNESS WHEREOF, the undersigned have executed this Agreement.


                              TYCO INTERNATIONAL LTD.

                              By:        /s/ MARK H. SWARTZ      
                                 -----------------------------------------
                                 Name: Mark H. Swartz
                                 Title: Executive Vice President, Chief
                                        Financial Officer


                              UNITED STATES SURGICAL CORPORATION

                              By:        /s/ MARK H. SWARTZ      
                                 -----------------------------------------
                                 Name: Mark H. Swartz
                                 Title: Vice President


                               (Page 7 of 7 Pages)