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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. 1)

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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.
                               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. 1

     This Amendment No. 1 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 (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. 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.

Item 4.   Terms of the Transaction.

          The information set forth in Item 4(a) is hereby amended and
supplemented as follows:

     The section of the Offer to Purchase captioned "United States Federal
Income Tax Consequences" is hereby amended and supplemented by deleting the
first paragraph thereof and amending and restating it with the following:


        "The following discussion addresses the material United States federal
    income tax considerations relating to this Offer. This summary does not
    address all aspects of United States federal income taxation that may be
    relevant to a holder in light of the holder's personal circumstances. This
    discussion is based on provisions of the Internal Revenue Code of 1986, as
    amended (the "Code"), applicable Treasury Regulations promulgated or
    proposed thereunder ("Treasury Regulations"), judicial authority and current
    administrative rulings and practice, all of which are subject to change
    without notice, possibly on a retroactive basis, or to differing
    interpretation. This summary addresses the tax consequences to persons
    described below under "United States Holders" who hold Notes as "capital
    assets" (within the meaning of Section 1221 of the Code) and does not
    address tax considerations for non-United States holders or those tax
    considerations applicable to investors that may be subject to special tax
    rules, such as banks and other financial institutions; regulated investment
    companies; tax-exempt organizations; expatriates; insurance companies;
    traders or dealers in securities or currencies; custodians, nominees or
    similar financial intermediaries holding Notes for others; persons that hold
    Notes as a position in a hedging transaction or other risk reduction
    transaction for tax purposes; persons who own an interest in a partnership
    or other pass through entity that holds Notes; or persons that have a
    "functional currency" other than the United States dollar. Amdocs has not
    sought any ruling from the Internal Revenue Service (the "IRS") with respect
    to the statements made and the conclusions reached in the following summary,
    and there can be no assurance that the IRS will agree with such statements
    and conclusions. In addition, this summary does not address any tax
    considerations that may arise under state, local or non-United States tax
    laws."

Item 11.  Additional Information.

          The information set forth in Item 11(b) is hereby amended and
supplemented as follows:

          The section of the Offer to Purchase captioned "Incorporation of
Certain Documents by Reference" is hereby amended by deleting the section and
replacing it in its entirety with the following:



     "The following documents, which have been filed by Amdocs
(File No. 001-14840) with the SEC, are incorporated herein by reference:


     o    Amdocs' Annual Report on Form 20-F for the fiscal year ended September
          30, 2003 filed on December 24, 2003; and


     o    Amdocs' report on Form 6-K containing its results for the quarterly
          period ended December 31, 2003, filed on February 17, 2004.


     The documents incorporated by reference herein (other than exhibits to such
documents that are not specifically incorporated by reference herein) are
available without charge to any person to whom this Notice of Put Right and
Offer to Purchase has been delivered upon written or oral request to Thomas G.
O'Brien, Secretary and Treasurer, Amdocs Inc., 1390 Timberlake Manor Parkway,
Chesterfield, Missouri 63017, telephone: (314) 212-8328."


                                   SIGNATURE

     After due inquiry and to the best of my knowledge and belief, I certify
that the information set forth in this Amendment No. 1 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: May 25, 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.*
(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.