UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549



                                  SCHEDULE 13G

                   Under the Securities Exchange Act of 1934*

                               (Amendment No. __ )

                          Alexion Pharmaceuticals, Inc.
                                (Name of Issuer)

                         Common Stock, $0.0001 par value
                         (Title of Class of Securities)

                                    015351109
                                 (CUSIP Number)

                                October 12, 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 the
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 ("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).



- -------------------                                           ------------------
CUSIP No. 015351109                   13G                     Page 2 of 10 Pages
- -------------------                                           ------------------
- ---------- ---------------------------------------------------------------------
1          NAME OF REPORTING PERSON
           S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

           Duquesne Capital Management, L.L.C.
- ---------- ---------------------------------------------------------------------
2          CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*             (a) [ ]
                                                                         (b) [X]
- ---------- ---------------------------------------------------------------------
3          SEC USE ONLY
- ---------- ---------------------------------------------------------------------
4          CITIZENSHIP OR PLACE OF ORGANIZATION

           Pennsylvania
- -------------------- ------ ----------------------------------------------------
                     5      SOLE VOTING POWER

                            0
                     ------ ----------------------------------------------------
     NUMBER OF       6      SHARED VOTING POWER
      SHARES
   BENEFICIALLY             1,642,936
     OWNED BY        ------ ----------------------------------------------------
       EACH          7      SOLE DISPOSITIVE POWER
     REPORTING
      PERSON                0
       WITH          ------ ----------------------------------------------------
                     8      SHARED DISPOSITIVE POWER

                            1,642,936
- ---------- ---------------------------------------------------------------------
9          AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

           1,642,936
- ---------- ---------------------------------------------------------------------
10         CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

           N/A
- ---------- ---------------------------------------------------------------------
11         PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

           5.3%
- ---------- ---------------------------------------------------------------------
12         TYPE OF REPORTING PERSON*

           OO
- ---------- ---------------------------------------------------------------------

                      *SEE INSTRUCTION BEFORE FILLING OUT!


                                      -2-



- -------------------                                           ------------------
CUSIP No. 015351109                   13G                     Page 3 of 10 Pages
- -------------------                                           ------------------
- ---------- ---------------------------------------------------------------------
1          NAME OF REPORTING PERSON
           S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

           Stanley F. Druckenmiller
- ---------- ---------------------------------------------------------------------
2          CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*             (a) [ ]
                                                                         (b) [X]
- ---------- ---------------------------------------------------------------------
3          SEC USE ONLY
- ---------- ---------------------------------------------------------------------
4          CITIZENSHIP OR PLACE OF ORGANIZATION

           United States
- -------------------- ------ ----------------------------------------------------
                     5      SOLE VOTING POWER

                            0
                     ------ ----------------------------------------------------
     NUMBER OF       6      SHARED VOTING POWER
      SHARES
   BENEFICIALLY             1,642,936
     OWNED BY        ------ ----------------------------------------------------
       EACH          7      SOLE DISPOSITIVE POWER
     REPORTING
      PERSON                0
       WITH          ------ ----------------------------------------------------
                     8      SHARED DISPOSITIVE POWER

                            1,642,936
- ---------- ---------------------------------------------------------------------
9          AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

           1,642,936
- ---------- ---------------------------------------------------------------------
10         CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

           N/A
- ---------- ---------------------------------------------------------------------
11         PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

           5.3%
- ---------- ---------------------------------------------------------------------
12         TYPE OF REPORTING PERSON*

           IN
- ---------- ---------------------------------------------------------------------

                      *SEE INSTRUCTION BEFORE FILLING OUT!


                                      -3-



- -------------------                                           ------------------
CUSIP No. 015351109                   13G                     Page 4 of 10 Pages
- -------------------                                           ------------------
- ---------- ---------------------------------------------------------------------
1          NAME OF REPORTING PERSON
           S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

           Steeler Fund, Ltd.
- ---------- ---------------------------------------------------------------------
2          CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*             (a) [ ]
                                                                         (b) [X]
- ---------- ---------------------------------------------------------------------
3          SEC USE ONLY
- ---------- ---------------------------------------------------------------------
4          CITIZENSHIP OR PLACE OF ORGANIZATION

           Cayman Islands
- -------------------- ------ ----------------------------------------------------
                     5      SOLE VOTING POWER

                            0
                     ------ ----------------------------------------------------
     NUMBER OF       6      SHARED VOTING POWER
      SHARES
   BENEFICIALLY             1,576,936
     OWNED BY        ------ ----------------------------------------------------
       EACH          7      SOLE DISPOSITIVE POWER
     REPORTING
      PERSON                0
       WITH          ------ ----------------------------------------------------
                     8      SHARED DISPOSITIVE POWER

                            1,576,936
- ---------- ---------------------------------------------------------------------
9          AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

           1,576,936
- ---------- ---------------------------------------------------------------------
10         CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

           N/A
- ---------- ---------------------------------------------------------------------
11         PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

           5.1%
- ---------- ---------------------------------------------------------------------
12         TYPE OF REPORTING PERSON*

           OO
- ---------- ---------------------------------------------------------------------

                      *SEE INSTRUCTION BEFORE FILLING OUT!


                                      -4-



This statement on Schedule 13G is filed with respect to the Common Stock (as
defined in Item 2(d) below) of Alexion Pharmaceuticals, Inc., a corporation
organized under the laws of the State of Delaware.

Item 1(a):     Name of Issuer:
- ---------      --------------

     The name of the issuer is Alexion Pharmaceuticals, Inc. (the "Company").

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

     The Company's principal executive office is located at 352 Knotter Drive,
Cheshire, Connecticut 06410.

Item 2(a):     Name of Person Filing:
- ---------      ---------------------

     This Schedule 13G (this "Schedule 13G") with respect to the Common Stock of
the Company is filed by:

     1.   Duquesne Capital Management, L.L.C., a Pennsylvania limited liability
          company ("Duquesne Capital"), which serves as the investment manager
          to Steeler Fund, Ltd., a Cayman Islands exempted limited liability
          company ("Steeler"), and several other investment funds (the "Funds"),
          with respect to shares of Common Stock directly beneficially owned by
          the Funds (collectively, the "Shares"); and

     2.   Mr. Stanley F. Druckenmiller ("Mr. Druckenmiller"), who serves as the
          managing member of Duquesne Capital, with respect to the Shares. Mr.
          Druckenmiller also serves as the managing member of Duquesne Holdings,
          LLC, a limited liability company organized under the laws of Anguilla,
          British West Indies ("Duquesne Holdings"), which acts as general
          partner to certain of the Funds, and which has the power to replace
          Duquesne Capital as investment manager of Steeler and of those Funds
          within 60 days or less; and

     3.   Steeler, with respect to shares of Common Stock directly held by it.

     Duquesne Capital may be deemed to beneficially own the Shares by virtue of
its position as investment manager of the Funds. Mr. Druckenmiller may be deemed
to beneficially own the Shares by virtue of his position as managing member of
Duquesne Capital, and as managing member of Duquesne Holdings. Duquesne Capital,
Mr. Druckenmiller and Steeler are hereinafter sometimes collectively referred to
as the "Reporting Persons." Any disclosures herein with respect to persons other
than the Reporting Persons are made on information and belief after making
inquiry to the appropriate party.


                                      -5-



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

     The address of the principal business office of Duquesne Capital and Mr.
Druckenmiller is 40 West 57th Street, 25th Floor, New York, New York 10019. The
address of the principal business office of Steeler is 2nd Floor, Harbour
Centre, Georgetown, Grand Cayman.

Item 2(c):     Citizenship:
- ---------      -----------

     Duquesne Capital is organized under the laws of the Commonwealth of
Pennsylvania. Mr. Druckenmiller is a citizen of the United States of America.
Steeler is organized under the laws of the Cayman Islands.

Item 2(d):     Title of Class of Securities:
- ---------      ----------------------------

     Common Stock, par value $0.0001 ("Common Stock").

Item 2(e):     CUSIP Number:
- ----------     ------------

     015351109

Item 3:        If this statement is filed pursuant to Rules 13d-1(b) or 13d-2(b)
- ------         -----------------------------------------------------------------
               or (c), check whether the person filing is a:
               --------------------------------------------

               A.   [ ] Broker or dealer registered under Section 15 of the Act,
               B.   [ ] Bank as defined in Section 3(a)(6) of the Act,
               C.   [ ] Insurance Company as defined in Section 3(a)(19) of the
                        Act,
               D.   [ ] Investment Company registered under Section 8 of the
                        Investment Company Act of 1940,
               E.   [ ] Investment Adviser in accordance with Rule 13d-1
                        (b)(1)(ii)(E),
               F.   [ ] Employee Benefit Plan or Endowment Fund in accordance
                        with 13d-1 (b)(1)(ii)(F),
               G.   [ ] Parent Holding Company or control person in accordance
                        with Rule 13d-1 (b)(1)(ii)(G),
               H.   [ ] Savings Association as defined in Section 3(b) of the
                        Federal Deposit Insurance Act,
               I.   [ ] 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).


                                      -6-



Item 4:        Ownership:
- ------         ---------

     A.   Duquesne Capital
          ----------------

          (a)  Amount beneficially owned: 1,642,936.
          (b)  Percent of class: 5.3%. The percentages used herein and in the
               rest of this Schedule 13G are calculated based upon a total of
               30,790,694 shares of Common Stock issued and outstanding as of
               September 30, 2005, as reflected in the Company's Annual Report
               on Form 10-K for the fiscal year ended July 31, 2005.
          (c)  Number of shares as to which such person has:
               (i)  Sole power to vote or direct the vote: -0-
               (ii) Shared power to vote or direct the vote: 1,642,936
               (iii) Sole power to dispose or direct the disposition: -0-
               (iv) Shared power to dispose or direct the disposition: 1,642,936

     B.   Mr. Druckenmiller
          -----------------

          (a)  Amount beneficially owned: 1,642,936
          (b)  Percent of class: 5.3%.
          (c)  Number of shares as to which such person has:
               (i)  Sole power to vote or direct the vote: -0-
               (ii) Shared power to vote or direct the vote: 1,642,936
               (iii) Sole power to dispose or direct the disposition: -0-
               (iv) Shared power to dispose or direct the disposition: 1,642,936

     C.   Steeler
          -------

          (a)  Amount beneficially owned: 1,576,936
          (b)  Percent of class: 5.1%.
          (c)  Number of shares as to which such person has:
               (i)  Sole power to vote or direct the vote: -0-
               (ii) Shared power to vote or direct the vote: 1,576,936
               (iii) Sole power to dispose or direct the disposition: -0-
               (iv) Shared power to dispose or direct the disposition: 1,576,936

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: [ ]


                                      -7-



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

     Other than as set forth herein, no other person is known to have the right
to receive or the power to direct the receipt of dividends from, or proceeds
from the sale of, the securities reported in this Schedule 13G.

Item 7:        Identification and Classification of the Subsidiary Which
               ---------------------------------------------------------
               Acquired the Security Being Reported on by the Parent Holding
               -------------------------------------------------------------
               Company:
               -------

     Not applicable.

Item 8:        Identification and Classification of Members of the Group:
- ------         ---------------------------------------------------------

     Not applicable.

Item 9:        Notice of Dissolution of Group:
               ------------------------------

     Not applicable.

Item 10:       Certification:
- -------        -------------

     Each Reporting Person hereby makes the following 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.


                                      -8-



                                    SIGNATURE

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

DATED:  October 21, 2005

                                 DUQUESNE CAPITAL MANAGEMENT, L.L.C.

                                 By:   /s/ Gerald Kerner
                                      ------------------------------------------
                                      Name:  Gerald Kerner
                                      Title: Managing Director


                                 STANLEY F. DRUCKENMILLER

                                 By:   /s/ Gerald Kerner
                                      ------------------------------------------
                                      Name:  Gerald Kerner
                                      Title: Attorney-in-Fact


                                 STEELER FUND, LTD.

                                 By:  Duquesne Capital Management, L.L.C.,
                                      its investment manager

                                 By:   /s/ Gerald Kerner
                                      ------------------------------------------
                                      Name:  Gerald Kerner
                                      Title: Managing Director







                 [SIGNATURE PAGE TO SCHEDULE 13G WITH RESPECT TO
                         ALEXION PHARMACEUTICALS, INC.]



                                  EXHIBIT INDEX

Exhibit 99.1:  Joint Filing Agreement, by and among Duquesne Capital Management,
               L.L.C., Stanley F. Druckenmiller and Steeler Fund, Ltd., dated
               October 21, 2005.

Exhibit 99.2:  Power of Attorney granted by Mr. Stanley F. Druckenmiller in
               favor of Gerald Kerner and Joseph W. Haleski, dated April 24,
               2002.

                                                                    Exhibit 99.1
                                                                    ------------

                             Joint Filing Agreement

     The undersigned hereby agree that the statement on Schedule 13G with
respect to the common stock of Alexion Pharmaceuticals, Inc. is, and any
amendment thereto signed by each of the undersigned shall be, filed on behalf of
each undersigned pursuant to and in accordance with the provisions of 13d-1(k)
under the Securities Exchange Act of 1934 and that all subsequent amendments to
this statement on Schedule 13G shall be filed on behalf of each of the
undersigned without the necessity of filing additional joint filing agreements.
The undersigned acknowledge that each shall be responsible for the timely filing
of such amendments, and for the completeness and accuracy of the information
concerning it contained therein, but shall not be responsible for the
completeness and accuracy of the information concerning the other, except to the
extent that it knows or has reason to believe that such information is
inaccurate.

DATED:  October 21, 2005

                                 DUQUESNE CAPITAL MANAGEMENT, L.L.C.

                                 By:   /s/ Gerald Kerner
                                      ------------------------------------------
                                      Name:  Gerald Kerner
                                      Title: Managing Director


                                 STANLEY F. DRUCKENMILLER

                                 By:   /s/ Gerald Kerner
                                      ------------------------------------------
                                      Name:  Gerald Kerner
                                      Title: Attorney-in-Fact


                                 STEELER FUND, LTD.

                                 By:  Duquesne Capital Management, L.L.C.,
                                      its investment manager

                                 By:   /s/ Gerald Kerner
                                      ------------------------------------------
                                      Name:  Gerald Kerner
                                      Title: Managing Director

                                                                    Exhibit 99.2
                                                                    ------------


                                Power of Attorney

KNOW ALL MEN BY THESE PRESENTS, that I, STANLEY F. DRUCKENMILLER, hereby make,
constitute and appoint each of Gerald Kerner and Joseph W. Haleski acting
individually and with full power of substitution, as my agent and
attorney-in-fact for the purpose of executing in my name, (a) in my personal
capacity, (b) in my capacity as managing member or in other capacities with
Duquesne Capital Management, L.L.C., a Pennsylvania limited liability company
("Duquesne Capital") or (c) in my capacity as managing member or in other
capacities of Duquesne Holdings, LLC, a limited liability company organized
under the laws of Anguilla, British West Indies ("Duquesne Holdings"), and each
of their affiliates or entities advised or controlled by me, Duquesne Capital or
Duquesne Holdings, all documents, certificates, instruments, statements, filings
and agreements ("documents") to be filed with or delivered to any foreign or
domestic governmental or regulatory body or required or requested by any other
person or entity pursuant to any legal or regulatory requirement relating to the
acquisition, ownership, management or disposition of securities or other
investments, and any other documents relating or ancillary thereto, including
but not limited to, all documents relating to filings with the United States
Securities and Exchange Commission (the "Commission") pursuant to the Securities
Act of 1933, as amended, or the Securities Exchange Act of 1934 (the "Exchange
Act") and the rules and regulations promulgated thereunder, including: (1) all
documents relating to the beneficial ownership of securities required to be
filed with the Commission pursuant to Section 13(d) or Section 16(a) of the
Exchange Act including, without limitation: (a) any acquisition statements on
Schedule 13D or Schedule 13G and any amendments thereto, (b) any joint filing
agreements pursuant to Rule 13d-1(k), and (c) any initial statements of, or
statements of changes in, beneficial ownership of securities on Form 3, Form 4
or Form 5 and (2) any information statements on Form 13F required to be filed
with the Commission pursuant to Section 13(f) of the Exchange Act. All past acts
of the attorney-in-fact in furtherance of the foregoing are hereby ratified and
confirmed. This power of attorney shall be valid from the date hereof until
revoked by me.

IN WITNESS WHEREOF, I have executed this instrument as of the 24th day of April,
2002.


/s/ Stanley F. Druckenmiller
- ----------------------------
Stanley F. Druckenmiller