Exhibit (a)(5)(ii)

                  AMDOCS ANNOUNCES COMPLETION OF CASH OFFER FOR
                      2% CONVERTIBLE NOTES DUE JUNE 1, 2008

ST. LOUIS, MO, June 1, 2004 -- Amdocs Limited (NYSE: DOX), a leading provider of
billing and CRM products and services for true, integrated customer management,
today announced it has completed the cash offer for its 2% Convertible Notes due
June 1, 2008.

Pursuant to the indenture for the notes, each holder of the notes had the right
to require Amdocs to repurchase on June 1, 2004 all or any part of such holder's
notes at a price equal to 100% of the principal amount plus accrued and unpaid
interest. Under the terms of the notes, Amdocs had the option to pay for the
notes with cash, ordinary shares, or a combination of cash and ordinary shares,
and elected to pay for the notes solely with cash. Amdocs commenced a cash offer
to the holders of the notes on May 3, 2004. The note holders' option to
surrender their notes for repurchase ended today at 9:00 a.m., Eastern time.

Amdocs has been advised by the Paying Agent, The Bank of New York, that
$395,110,000 principal amount of the notes were surrendered for repurchase and
not withdrawn. Amdocs has accepted for payment all of those notes, resulting in
total payments in the amount of $395,110,000. Payment for the notes will be made
with available cash. The untendered $344,000 principal amount of notes will
remain as obligations of the Company, due June 1, 2008, in accordance with their
terms.

About Amdocs

Amdocs combines innovative software products and services with deep business
knowledge to deliver true integrated customer management to the world's leading
services companies. Our best-in-class billing and CRM products seamlessly link
all customer-facing business processes - marketing, sales, ordering, delivery,
fulfillment, billing, settlement, service, support, and analytics - resulting in
stronger, more profitable customer relationships. Amdocs enables its customers
to implement their business strategy with rapid return on investment, lower
total cost of ownership and improved operational efficiencies. A global company,
Amdocs employs approximately 9,000 IT professionals and serves customers in more
than 40 countries. Amdocs reported revenue of nearly $1.5 billion in fiscal
2003. For more information, visit Amdocs at www.amdocs.com.

Contact:
Thomas G. O'Brien
Treasurer and Vice President of Finance and Investor Relations
Amdocs Limited
314-212-8328
E-mail: dox_info@amdocs.com