<PAGE>   1
                                                                    Exhibit 99.1

AMDOCS LIMITED REPORTS 54% INCREASE IN FOURTH QUARTER OPERATING INCOME --Annual
               Revenue Exceeds $400 Million for the First Time--

St. Louis, MO - November 11, 1998, Amdocs Limited (NYSE: DOX) today reported
results for the fourth quarter and year ended September 30, 1998. For the
quarter, revenue increased by 32.6% to $116.7 million while operating income
grew 53.8%. Net income reached $11.6 million, or $0.06 per diluted share.

Avi Naor, Chief Executive Officer of Amdocs Management Limited, noted, "While
impressive, these quarterly results are indicative of how Amdocs has performed
over its 17 year history. We have consistently implemented our strategy of
providing the best products and solutions for new and existing
telecommunications customers in both new and existing markets. As indicated by
our top and bottom line growth this quarter, we have a strategy that works,
making us the choice of telecom leaders. These leaders rely on Amdocs because we
supply full solutions combining products, implementation and support services,
and have the highest commitment to maintaining such working methods over time."

Naor continued, "1998 was a terrific year for Amdocs. In addition to our initial
public offering this summer, we made significant headway in penetrating new
markets and adding new customers. These include leading telecommunications
providers, expanding companies that have outgrown legacy systems and emerging
carriers with high growth potential. These new clients further enrich an already
top-notch group of companies with which we have a history of maintaining
productive long-term relationships."

"Annual revenue exceeded a milestone $400 million for the first time, reflecting
a high demand for top-of-the-line customer care and billing systems," Naor
noted. "Telecommunications remains an explosive growth market globally and
demand for Amdocs systems from our market-leading customers remains high."

"Amdocs also continues to benefit from industry consolidation. As
telecommunications companies increase in size, they need our systems with
unlimited scalability and rich functionality to support expanding customer
populations and provide a strategic edge in highly competitive markets," Naor
added.

Naor concluded, "Due to favorable market conditions, leading products, excellent
customer relationships and a track record of reliability, our forward visibility
and confidence remain high as we enter the first quarter of fiscal 1999."

The company noted that during the fourth quarter of its fiscal year, it
experienced strong revenue contribution from its customer care and billing
business, which grew 49.5%.

Operating income increased 53.8% to $26.1 million compared to operating income
before nonrecurring charges of $17.0 million in the fourth quarter of 1997.

Net income for the three months increased to $11.6 million and was favorably
impacted by a reduction in quarterly interest expense due to the repayment of
long-term debt from proceeds of the company's initial 
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public offering. Diluted earnings per share for the quarter ended September 30,
1998, were $0.06 based on 198,361,000 weighted average shares outstanding.

For the year ended September 30, 1998, revenue grew by 39.2% to a record $403.8
million compared to $290.1 million reported for the prior year. Fiscal 1998
revenue reflected a 65.0% increase in license revenue.

Operating income for fiscal 1998 increased 55.7% to $84.9 million from $54.5
million before nonrecurring charges in 1997. As a percentage of sales, annual
operating margins increased to 21.0% from 18.8% in fiscal 1997.

Net income for the year reached $30.1 million compared to $5.9 million for the
prior year. Diluted earnings per share for fiscal 1998 were $0.19 compared to
diluted earnings per share inclusive of nonrecurring charges of $0.05 in fiscal
1997.

Amdocs is a leading provider of product-driven customer care and billing
solutions to premier telecommunications companies worldwide. Amdocs has an
unparalleled success record in project delivery of its mission-critical
products. With human resources of over 2,900 information systems professionals
dedicated to the telecommunications industry, Amdocs has an installed base of
successful projects with more than 60 major telecommunications companies
throughout the world.

For more information visit our Web site at www.amdocs.com.

THIS PRESS RELEASE MAY CONTAIN FORWARD-LOOKING STATEMENTS AS DEFINED UNDER THE
SECURITIES ACT OF 1933, AS AMENDED. SUCH STATEMENTS INVOLVE RISKS AND
UNCERTAINTIES THAT MAY CAUSE FUTURE RESULTS TO DIFFER FROM THOSE ANTICIPATED.
THESE RISKS INCLUDE, BUT ARE NOT LIMITED TO, THE ADVERSE EFFECTS OF MARKET
COMPETITION, RAPID CHANGES IN TECHNOLOGY THAT MAY RENDER THE COMPANY'S PRODUCTS
AND SERVICES OBSOLETE, POTENTIAL LOSS OF A MAJOR CUSTOMER, AND RISKS ASSOCIATED
WITH OPERATING BUSINESSES IN THE INTERNATIONAL MARKET. THESE AND OTHER RISKS ARE
DISCUSSED AT GREATER LENGTH IN THE COMPANY'S QUARTERLY FILINGS ON FORM 6-K AND
ANNUAL FILING ON FORM 20-F WITH THE SECURITIES AND EXCHANGE COMMISSION.

                           (FINANCIAL TABLES FOLLOW)
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AMDOCS LIMITED

CONSOLIDATED BALANCE SHEETS
(in thousands)

<TABLE>
<CAPTION>
                                                           September 30,
                                                           -------------
                                                          1998       1997
                                                          ----       ----
<S>                                                     <C>        <C>    

                       ASSETS

Current Assets:
  Cash and cash equivalents                             $25,389    $53,732
  Accounts receivable, including unbilled of
   $10,331 in 1998 and $2,031 in 1997                    79,723     48,565
  Accounts receivable from related parties,
   including unbilled of $537 in 1998 and $0 in 1997     10,235     15,393
  Deferred income taxes                                  14,534     12,532
  Prepaid expenses and other current assets              11,991      6,161
                                                        -------    -------
    Total current assets                                141,872    136,383

Equipment, vehicles and leasehold improvements, net      46,404     28,287
Deferred income taxes                                     7,773      4,587
Intellectual property rights                             23,362     25,982
Other noncurrent assets                                  20,555     25,343
                                                        --------  --------
                                                       $239,966   $220,582
                                                       ========   ========

              LIABILITIES AND SHAREHOLDERS' EQUITY (DEFICIT)

Current Liabilities:
  Accounts payable and accrued expenses                 $47,599    $30,543
  Accrued personnel costs                                29,948     23,098
  Short-term financing arrangements                      91,565      1,998
  Unearned revenue                                       29,241     17,440
  Notes payable to related parties                            -      3,268
  Short-term portion of capital lease obligations         2,952      1,954
  Forward exchange contracts                              2,926          -
  Income taxes payable and deferred income taxes         21,919     20,151
                                                        -------    -------
    Total current liabilities                           226,150     98,452
Long-term forward exchange contracts                      2,222          -
Long-term portion of capital lease obligations            9,215      7,370
Other noncurrent liabilities                             24,268     20,507
Shareholders' equity (deficit):
  Preferred Shares - 0 shares issued and outstanding          -          -
  Ordinary Shares - 196,800 and 124,708 issued and
  outstanding, respectively                               3,149      1,996
  Additional paid-in capital                            447,503    105,779
  Unrealized loss on derivative instruments              (1,495)         -
  Unearned compensation                                  (8,947)         -
</TABLE>
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<TABLE>
<CAPTION>
                                                           September 30,
                                                           -------------
                                                          1998       1997
                                                          ----       ----
<S>                                                    <C>        <C>    
  Accumulated deficit                                  (462,099)   (13,522)
                                                       --------   --------
    Total shareholders' equity (deficit)                (21,889)    94,253
                                                       ========   ========
                                                       $239,966   $220,582
                                                       ========   ========
</TABLE>
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AMDOCS LIMITED

CONSOLIDATED STATEMENTS OF OPERATIONS
(in thousands, except per share data)

<TABLE>
<CAPTION>
                                                                 Three months ended                    Year ended          
                                                                    September 30,                     September 30,
                                                                    -------------                     -------------
                                                                1998            1997              1998            1997
                                                                ----            ----              ----            ----
                                                                     (unaudited)
<S>                                                           <C>             <C>              <C>             <C>      
Revenue:                                                      
  License                                                     $  13,150       $  10,427        $  42,891       $  25,995
  Service                                                       103,554          77,560          360,876         264,107
                                                              ---------       ---------        ---------       ---------
                                                                116,704          87,987          403,767         290,102
                                                              
Operating expenses:                                           
  Cost of license                                                 2,211            (169)          10,732           3,711
  Cost of service                                                66,092          51,575          231,360         173,704
  Research and development                                        7,485           5,208           25,612          17,386
  Selling, general and administrative                            14,812          14,396           51,168          40,769
  Nonrecurring charges                                             --            27,563               --          27,563
                                                              ---------       ---------        ---------       ---------
                                                                 90,600          98,573          318,872         263,133
                                                              ---------       ---------        ---------       ---------
Operating income (loss)                                          26,104         (10,586)          84,895          26,969
                                                              
Other expense, net                                                2,354           3,116           24,126           3,266
                                                              ---------       ---------        ---------       ---------
Income (loss) before income taxes                                23,750         (13,702)          60,769          23,703
Income tax expense                                               11,875           4,605           30,385          17,827
                                                              ---------       ---------        ---------       ---------
Net income (loss) before                                         11,875         (18,307)          30,384           5,876
cumulative effect                                             
Cumulative effect of changes in                               
accounting principle, net of $277 tax                               277            --                277            --
                                                              ---------       ---------        ---------       ---------
Net income (loss)                                             $  11,598       $ (18,307)       $  30,107       $   5,876
                                                              ---------       ---------        ---------       ---------
                                                             
Basic earnings (loss) per share                               
  Income (loss) before cumulative effect                      $    0.06       $   (0.17)       $    0.19       $    0.05
  Cumulative effect of a change                               
  in accounting principle (less than $0.01)                          --              --               --              --
                                                              ---------       ---------        ---------       ---------
  Net income (loss)                                           $    0.06       $   (0.17)       $    0.19       $    0.05
                                                              ---------       ---------        ---------       ---------
                                                              
Diluted earnings (loss) per share                             
  Income (loss) before cumulative effect                      $    0.06       $   (0.17)       $    0.19       $    0.05
  Cumulative effect of a change in                            
    accounting principle (less than $0.01)                           --              --               --              --
                                                              ---------       ---------        ---------       ---------
  Net income (loss)                                           $    0.06       $   (0.17)       $    0.19       $    0.05
                                                              ---------       ---------        ---------       ---------
                                                              
Weighted average diluted shares outstanding                     198,361         112,143          159,442         110,915
</TABLE>