SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM 6-K

                        REPORT OF FOREIGN PRIVATE ISSUER
                      PURSUANT TO RULE 13A-16 OR 15D-16 OF
                       THE SECURITIES EXCHANGE ACT OF 1934

                        For the month of September, 2004

                         Commission File Number 1-14840

                                 AMDOCS LIMITED

                      Suite 5, Tower Hill House Le Bordage
           St. Peter Port, Island of Guernsey, GY1 3QT Channel Islands

                                  Amdocs, Inc.
           1390 Timberlake Manor Parkway, Chesterfield, Missouri 63017

                    (Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports
under cover of Form 20-F or Form 40-F:

                 FORM 20-F     X                FORM 40-F
                            -------                       -------

Indicate by check mark whether the registrant by furnishing the information
contained in this form is also thereby furnishing the information to the
Commission pursuant to rule 12g3-2(b) under the Securities Exchange Act of 1934:

                        YES                     NO     X
                            -------                 -------


     The Registrant is filing this Current Report on Form 6-K for the purpose of
filing with the Securities and Exchange Commission (the "SEC") the Customer Care
and Billing Services Agreement, between Nextel Finance Company and Amdocs
Software Systems Limited, a wholly owned subsidiary of the Registrant, dated as
of January 1, 2000, as amended (the "Agreement"). The Agreement is attached to
this Form 6-K as Exhibit 99.1.

     This Form 6-K shall be incorporated by reference into the Registration
Statements on Form F-3 (File Nos. 333-114079 and 333-114344) and any other
Registration Statement filed by the Registrant which by its terms automatically
incorporates the Registrant's filings and submissions with the SEC under
Sections 13(a), 13(c) or 15(d) of the Securities Exchange Act of 1934.


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                                   SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.

                                                  AMDOCS LIMITED


                                                  /s/ Thomas G. O'Brien
                                                  ------------------------------
                                                  Thomas G. O'Brien
                                                  Treasurer and Secretary
                                                  Authorized U.S. Representative


Date:  September 30, 2004


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                                  EXHIBIT INDEX


EXHIBIT NO.            DESCRIPTION
-----------            -----------

   99.1+               Customer Care and Billing Services Agreement, between
                       Nextel Finance Company and Amdocs Software Systems
                       Limited, dated as of January 1, 2000, as amended.


+  Confidential treatment requested as to certain portions, which portions
   have been filed separately with the Securities and Exchange Commission.