SCHEDULE 13G


                       SECURITIES AND EXCHANGE COMMISSION
                              WASHINGTON, DC 20549


                    Under the Securities Exchange Act of 1934
                               (Amendment No.__)*

                          ALEXION PHARMACEUTICALS, INC.
 -------------------------------------------------------------------------------

                                (Name of Issuer)

                     Common Stock, par value $0.01 per share
 -------------------------------------------------------------------------------
|
                         (Title of Class of Securities)

                                   015351 10 9
          ------------------------------------------------------------

                                 (CUSIP Number)

                                  June 17, 2005
          ------------------------------------------------------------
             (Date of Event which Requires Filing of this Statement)
 
                 Check the appropriate box to designate the rule pursuant to
which this Schedule is filed:

                  |_|  Rule 13d-1(b)

                  |X|  Rule 13d-1(c)

                  |_|  Rule 13d-1(d)

                  *The remainder of this cover page shall be filled out for a
         reporting person's initial filing on this form with respect to the
         subject class of securities, and for any subsequent amendment
         containing information which would alter disclosures provided in a
         prior cover page.

                  The information required on the remainder of this cover page
         shall not be deemed to be "filed" for the purpose of Section 18 of the
         Securities Exchange Act of 1934 (the "Act") or otherwise subject to the
         liabilities of that section of the Act, but shall be subject to all
         other provisions of the Act (however, see the Notes).

                                Page 1 of 8 Pages



CUSIP No.  015351 10 9

--------------------------------------------------------------------------------

  1     NAMES OF REPORTING PERSONS
        I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (entities only)

         Felix J. Baker
--------------------------------------------------------------------------------

  2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (See Instructions) 
                                                                        (a) |_|
                                                                        (b) |X|

--------------------------------------------------------------------------------

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

  4     CITIZENSHIP OR PLACE OF ORGANIZATION

         United States
--------------------------------------------------------------------------------

       NUMBER OF           5    SOLE VOTING POWER
         SHARES
      BENEFICIALLY                    -0-
        OWNED BY         -------------------------------------------------------
          EACH                                                                  
       REPORTING           6    SHARED VOTING POWER                             
         PERSON                                                                 
          WITH                         1,613,027                                
                         -------------------------------------------------------
                                                                                
                           7    SOLE DISPOSITIVE POWER                          
                                                                                
                                          -0-                                   
                         -------------------------------------------------------
                                                                                
                           8    SHARED DISPOSITIVE POWER                        
                                                                                
                                        1,613,027                               
--------------------------------------------------------------------------------

  9     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

               1,613,027
--------------------------------------------------------------------------------

  10    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES    
        (See Instructions)                                                  |_|
--------------------------------------------------------------------------------

  11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

            5.5%
--------------------------------------------------------------------------------

  12    TYPE OF REPORTING PERSON (See Instructions)
             IN

--------------------------------------------------------------------------------

                                Page 2 of 8 Pages



CUSIP No.  015351 10 9

--------------------------------------------------------------------------------

  1     NAMES OF REPORTING PERSONS
        I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (entities only)

         Julian C. Baker
--------------------------------------------------------------------------------

  2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (See Instructions)     
                                                                        (a) |_|
                                                                        (b) |X|
--------------------------------------------------------------------------------

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

  4     CITIZENSHIP OR PLACE OF ORGANIZATION

         United States
--------------------------------------------------------------------------------

     NUMBER OF        5    SOLE VOTING POWER
      SHARES
   BENEFICIALLY                  -0-
     OWNED BY       ------------------------------------------------------------
       EACH                                                                     
     REPORTING        6    SHARED VOTING POWER                                  
      PERSON                                                                    
       WITH                       1,613,027                                     
--------------------------------------------------------------------------------
                                                                                
                      7    SOLE DISPOSITIVE POWER                               
                                                                                
                                     -0-                                        
--------------------------------------------------------------------------------
                                                                                
                      8    SHARED DISPOSITIVE POWER                             
                                                                                
                                  1,613,027                                     
--------------------------------------------------------------------------------

  9     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

               1,613,027
--------------------------------------------------------------------------------

  10    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES    
        (See Instructions)                                                  |_|
--------------------------------------------------------------------------------

  11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

            5.5%
--------------------------------------------------------------------------------

  12    TYPE OF REPORTING PERSON (See Instructions)
             IN

--------------------------------------------------------------------------------

                                Page 3 of 8 Pages



Item 1(a)         Name of Issuer:

                  Alexion Pharmaceuticals, Inc.

Item 1(b)         Address of Issuer's Principal Executive Offices:

                  352 Knotter Drive
                  Cheshire, Connecticut  06410

Item 2(a)         Name of Person Filing:

                  This Schedule 13G is being filed jointly by Felix J. Baker and
                  Julian C. Baker (the "Reporting Persons").

Item 2(b)         Address of Principal Business Office or, if None, Residence:

                  Name                             Business Address
                  ----                             ----------------

                  Felix J.Baker                    667 Madison Avenue
                                                   New York, NY 10021

                  Julian C. Baker                  667 Madison Avenue
                                                   New York, NY 10021
Item 2(c)         Citizenship:

                  Each of the Reporting Persons is a United States citizen.

Item 2(d)         Title of Class of Securities:

                  Common Stock, par value $0.01 per share

Item 2(e)         CUSIP Number:

                  015351 10 9

Item 3.           If this statement is filed pursuant to ss.ss.240.13d-1(b) or 
                  (c), check whether the person filing is a:   N/A

         (a) [ ] Broker or dealer registered under Section 15 of the Exchange
Act;

         (b) [ ] Bank as defined in section 3(a)(6) of the Exchange Act;

         (c) [ ] Insurance company as defined in section 3(a)(19) of the
Exchange Act;

         (d) [ ] Investment company registered under section 8 of the Investment
Company Act of 1940;

         (e) [ ] An investment adviser in accordance with Rule
13d-1(b)(1)(ii)(E);

                                Page 4 of 8 Pages



         (f) [ ] An employee benefit plan or endowment fund in accordance with
Rule 13d-1(b)(1)(ii)(F);

         (g) [ ] A parent holding company or control person in accordance with
Rule 13d-1(b)(1)(ii)(G).

         (h) [ ] A savings association as defined in Section 3(b) of the Federal
Deposit Insurance Act.

         (i) [ ] A church plan that is excluded from the definition of an
investment company under section 3(c)(14) of the Investment Company Act of 1940.

         (j) [ ] Group, in accordance with Rule 13d-1(b)(1)(ii)(J).

Item 4.           Ownership.

                  Set forth below is the aggregate number of shares of Common
Stock, including shares that may be acquired upon conversion of 1.375%
Convertible Notes due February 2012 at the presently applicable conversion price
of $31.46, held as of the date hereof by each of the following, together with
the percentage of the outstanding shares of Common Stock that such number
represents based upon 28,091,000 shares as of July 19, 2005, as reported on the
Company's Form 10-Q for the quarterly period ended April 30, 2005.



                                                                                     Percent of Class
          Name                                                   Number of Shares      Outstanding
          --------------------------------                       --------------      -----------
                                                                                      
          Baker/Tisch Investments, L.P.                                  41,216             0.1%
          Baker Bros. Investments, L.P.                                  49,783             0.2%
          Baker Bros. Investments II, L.P.                               42,751             0.2%
          Baker Biotech Fund I, L.P.                                    493,499             1.7%
          Baker Biotech Fund II, L.P.                                   450,691             1.6%
          Baker Biotech Fund II (Z), L.P.                                56,453             0.2%
          Baker Biotech Fund III, L.P.                                  370,348             1.3%
          Baker Biotech Fund III (Z), L.P.                               77,233             0.3%
          14159, L.P.                                                    31,053             0.1%
          --------------------------------                          -----------          -------
          Total                                                      1,613,027             5.5%


                           By virtue of their ownership of entities that have
the power to control the investment decisions of the limited partnerships listed
in the table above, Felix J. Baker and Julian C. Baker may each be deemed to be
beneficial owners of securities owned by such entities and may be deemed to have
shared power to vote or direct the vote of and shared power to dispose or direct
the disposition of such securities.

                                Page 5 of 8 Pages



Item 5.           Ownership of Five Percent or Less of a Class.

                  If this statement is being filed to report the fact that as of
the date hereof the reporting person has ceased to be the beneficial owner of
more than five percent of the class of securities, check the following [ ]. N/A

Item 6.           Ownership of More than Five Percent on Behalf of Another 
                  Person.

                  The entities listed in Item 4 above are investment funds the
investors in which have the right to receive dividends, interest and the
proceeds of sale of securities owned by such funds.

Item 7.           Identification and Classification of the Subsidiary Which 
                  Acquired the Security Being Reported on by the Parent Holding 
                  Company or Control Person.

                  N/A

Item 8.           Identification and Classification of Members of the Group.

                  N/A

Item 9.           Notice of Dissolution of Group.

                  N/A

Item 10.          Certification.

                  By signing below I certify that, to the best of my knowledge
and belief, the securities referred to above were not acquired and are not held
for the purpose of or with the effect of changing or influencing the control of
the issuer of the securities and were not acquired and are not held in
connection with or as a participant in any transaction having that purpose or
effect.

                                Page 6 of 8 Pages



                                    SIGNATURE

                  After reasonable inquiry and to the best of my knowledge and
belief, I hereby certify that the information set forth in this statement is
true, complete and correct.

July 19, 2005

                                           /s/ Felix J. Baker
                                           ----------------------------------
                                           Felix J. Baker


                                           /s/ Julian C. Baker
                                           ----------------------------------
                                           Julian C. Baker

                                Page 7 of 8 Pages



                                    AGREEMENT


                  In accordance with Rule 13d-1(k)(1) under the Securities
Exchange Act of 1934, as amended, the undersigned hereby agree that this
Statement on Schedule 13G relating to the Common Stock of Insmed Incorporated is
being filed with the Securities and Exchange Commission on behalf of each of
them.

July 19, 2005

                                         /s/ Felix J. Baker
                                         ----------------------------------
                                         Felix J. Baker


                                         /s/ Julian C. Baker
                                         ----------------------------------
                                         Julian C. Baker

                                Page 8 of 8 Pages