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                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
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                                   SCHEDULE TO
                                 (RULE 14d-100)

            TENDER OFFER STATEMENT UNDER SECTION 14(d)(1) OR 13(e)(1)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

                                (AMENDMENT NO. 2)

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                                 AMDOCS LIMITED
                       (Name of Subject Company (Issuer))

                                 AMDOCS LIMITED
                       (Name of Filing Persons (Offeror))

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                      2% CONVERTIBLE NOTES DUE JUNE 1, 2008
                         (Title of Class of Securities)

                                   02342TAB52
                                   02342TAA79
                      (CUSIP Number of Class of Securities)

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                                  AMDOCS, INC.
           1390 TIMBERLAKE MANOR PARKWAY, CHESTERFIELD, MISSOURI 63017
                     ATTENTION: THOMAS G. O'BRIEN, TREASURER
                                 (314) 212-8328
(Name, address and telephone numbers of person authorized to receive notices and
                  communications on behalf of filing persons))

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      THE COMMISSION IS REQUESTED TO SEND COPIES OF ALL COMMUNICATIONS TO:

                             ROBERT A. SCHWED, ESQ.
                    WILMER CUTLER PICKERING HALE AND DORR LLP
                                 300 PARK AVENUE
                            NEW YORK, NEW YORK 10022
                                 (212) 937-7200

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[X]   Check the box if any part of the fee is offset as provided by Rule
      0-11(a)(2) and identify the filing with which the offsetting fee was
      previously paid. Identify the previous filing by registration statement
      number, or the Form or Schedule and the date of its filing.

      Amount Previously Paid: $50,105.             Filing party: Amdocs Limited.
      Form or Registration No.: Schedule TO-I.     Date filed: May 3, 2004.

[ ]   Check the box if the filing relates solely to preliminary communications
      made before the commencement of a tender offer.

Check the appropriate boxes below to designate any transactions to which the
statement relates:

[ ]   third party tender offer subject to Rule 14d-1.
[X]   issuer tender offer subject to Rule 13e-4.
[ ]   going-private transaction subject to Rule 13e-3.
[ ]   amendment to Schedule 13D under Rule 13d-2.

Check the following box if the filing is a final amendment reporting the results
of the tender offer: [ ]

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                    INTRODUCTORY STATEMENT TO AMENDMENT NO. 2


      This Amendment No. 2, the final amendment in connection herewith, amends
and supplements the Tender Offer Statement on Schedule TO-I filed by Amdocs
Limited, a company organized under the laws of the Island of Guernsey
("Amdocs"), with the Securities and Exchange Commission on May 3, 2004, as
amended and supplemented on May 25, 2004 (the "Schedule TO") relating to an
offer to purchase for cash, on the terms and subject to the conditions set forth
in the Notice of Put Right and Offer to Purchase, dated May 3, 2004 (as it may
be supplemented or amended from time to time, the "Offer to Purchase"), and the
related Letter of Transmittal (as it may be supplemented or amended from time to
time, the "Letter of Transmittal"), any and all of its outstanding 2%
Convertible Notes due June 1, 2008 (the "Notes"). Copies of the Offer to
Purchase and the Letter of Transmittal were previously filed as exhibits
(a)(1)(i) and (a)(1)(ii), respectively, to the Schedule TO. The Offer expired at
9:00 a.m., Eastern time, on June 1, 2004.

      Capitalized terms used in this amendment and not otherwise defined herein
have the meanings given to them in the Offer to Purchase and the Schedule TO.

ITEM 4. TERMS OF THE TRANSACTION.

      The information set forth in Item 4(a) is hereby amended and supplemented
by adding the following:

      "The Offer expired at 9:00 a.m., Eastern time, on Tuesday, June 1, 2004.
Amdocs has accepted for purchase $395,110,000 in aggregate principal amount of
the Notes, which constituted all of the Notes validly tendered and not
withdrawn, at a purchase price of $1,000 per $1,000 of principal amount of the
Notes. The purchase price applies to all of the Notes accepted for payment
pursuant to the Offer.

      On June 1, 2004 Amdocs issued a press release announcing the final results
of the Offer. A copy of this press release is filed as Exhibit (a)(5)(ii) to the
Schedule TO and is incorporated herein by reference."

ITEM 11. ADDITIONAL INFORMATION.

      The information set forth in Item 11(b) is hereby amended and supplemented
by incorporating by reference the information contained in Item 4 above.

ITEM 12.          EXHIBITS.

      The information set forth in Item 12 is hereby amended and supplemented by
adding immediately following the reference to Exhibit (a)(5)(ii) the following:

      "(a)(5)(ii) Press Release Regarding Results of the Offer, dated June 1,
2004."

                                    SIGNATURE

      After due inquiry and to the best of my knowledge and belief, I certify
that the information set forth in this Amendment No. 2 to Schedule TO is true,
complete and correct.

                                            AMDOCS LIMITED

                                            By:  /s/ Thomas G. O'Brien
                                                 -------------------------------
                                                  Thomas G. O'Brien
                                                  Treasurer and Secretary
                                                  Authorized U.S. Representative
Date: June 1, 2004

                                  EXHIBIT INDEX

         EXHIBIT
         NUMBER                    DESCRIPTION

         (a)(1)(i)      Notice of Put Right and Offer to Purchase, dated May 3,
                        2004.*

         (a)(1)(ii)     Letter of Transmittal, dated May 3, 2004.*

         (a)(1)(iii)    Letter to Clients, dated May 3, 2004.*

         (a)(1)(iv)     Letter to Brokers, Dealers, Commercial Banks, Trust
                        Companies and Other Nominees, dated May 3, 2004.*

         (a)(1)(v)      Guidelines to Form W-9.*

         (a)(5)(i)      Press Release Regarding Offer, dated May 3, 2004.*

         (a)(5)(ii)     Press Release Regarding Results of the Offer, dated June
                        1, 2004.

         (b)            None.

         (d)(1)         Indenture, dated as of May 30, 2001, between Amdocs
                        Limited and United States Trust Company of New York, as
                        trustee, for 2% Convertible Notes due June 1, 2008
                        (incorporated by reference to Exhibit 4.1 to Amdocs'
                        Report on Form 6-K, filed May 31, 2001).

         (d)(2)         Registration Rights Agreement, dated as of May 30, 2001,
                        between Amdocs Limited and Goldman, Sachs & Co.
                        (incorporated by reference to Exhibit 4.2 to Amdocs'
                        Report on Form 6-K, filed May 31, 2001).

         (g)            None.

         (h)            None.

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*  Previously Filed.