<PAGE>   1


================================================================================


                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM 10-Q

(Mark One)


[X]            QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF
                       THE SECURITIES EXCHANGE ACT OF 1934

                FOR THE QUARTERLY PERIOD ENDED DECEMBER 31, 1998

                                       OR


[ ]           TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF
                       THE SECURITIES EXCHANGE ACT OF 1934

            FOR THE TRANSITION PERIOD FROM __________ TO ___________

                        COMMISSION FILE NUMBER: 33-45417

                              THE BISYS GROUP, INC.

             (Exact name of registrant as specified in its charter)

<TABLE>
<S>                                                                                       <C>
                         DELAWARE                                                                     13-3532663

(State or other jurisdiction of incorporation or organization)                            (I.R.S. Employer Identification No.)
</TABLE>



                    150 CLOVE ROAD, LITTLE FALLS, NEW JERSEY
                                      07424

                    (Address of principal executive offices)
                                   (Zip Code)

                                  973-812-8600

              (Registrant's telephone number, including area code)


INDICATE BY CHECK MARK WHETHER THE REGISTRANT (1) HAS FILED ALL REPORTS REQUIRED
TO BE FILED BY SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934 DURING
THE PRECEDING 12 MONTHS (OR FOR SUCH SHORTER PERIOD THAT THE REGISTRANT WAS
REQUIRED TO FILE SUCH REPORT(S), AND (2) HAS BEEN SUBJECT TO SUCH FILING
REQUIREMENTS FOR THE PAST 90 DAYS.

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

INDICATE THE NUMBER OF SHARES OUTSTANDING OF EACH OF THE ISSUER'S CLASSES OF
COMMON STOCK, AS OF THE LATEST PRACTICABLE DATE:

                Class                    Shares Outstanding at January 25, 1999
--------------------------------------   --------------------------------------

Common Stock, par value $.02 per share                26,798,834
                                         --------------------------------------

                        This document contains  14 pages.
                                               ----

================================================================================

<PAGE>   2


                              THE BISYS GROUP, INC.

                               INDEX TO FORM 10-Q




<TABLE>
<CAPTION>
PART I.  FINANCIAL INFORMATION                                                                                   Page
<S>                                                                                                              <C>

         Item 1.  Financial Statements

                  Condensed Consolidated Balance Sheet as of December 31, 1998
                      and June 30, 1998                                                                            3

                  Condensed Consolidated Statement of Operations for the six months
                      ended December 31, 1998 and 1997                                                             4

                  Condensed Consolidated Statement of Cash Flows for the six months
                      ended December 31, 1998 and 1997                                                             5

                  Notes to Condensed Consolidated Financial Statements                                             6


         Item 2.  Management's Discussion and Analysis of Results of Operations and                                8
                  Financial Condition



PART II.  OTHER INFORMATION

         Item 4.  Submission of Matters to a Vote of Security Holders                                             12

         Item 6.  Exhibits and Reports on Form 8-K                                                                12

SIGNATURES                                                                                                        13

EXHIBIT INDEX                                                                                                     14
</TABLE>




                                       2
<PAGE>   3


                                     PART I

                          ITEM 1. FINANCIAL STATEMENTS

                     THE BISYS GROUP, INC. AND SUBSIDIARIES
                      CONDENSED CONSOLIDATED BALANCE SHEET
                  (DOLLARS IN THOUSANDS, EXCEPT PER SHARE DATA)
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                                                        December 31,           June 30,
                                                                                            1998                 1998
                                                                                        ------------           --------
<S>                                                                                       <C>                  <C>
ASSETS

Current assets:
  Cash and cash equivalents                                                               $ 36,943             $ 93,403
  Accounts receivable, net                                                                  84,960               73,693
  Deferred tax asset                                                                         4,421                4,660
  Prepaid expenses and other                                                                10,916                8,484
                                                                                          --------             --------
     Total current assets                                                                  137,240              180,240
Property and equipment, net                                                                 46,777               37,478
Intangible assets, net                                                                     142,255              102,663
Other assets                                                                                24,918               13,720
                                                                                          --------             --------
     Total assets                                                                         $351,190             $334,101
                                                                                          ========             ========

LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities
  Current maturities of long-term debt                                                    $     79             $    124
  Accounts payable                                                                          11,761               11,626
  Short-term borrowings                                                                     20,000                    -
  Other current liabilities                                                                 62,055               70,668
                                                                                          --------             --------
     Total current liabilities                                                              93,895               82,418
Long-term debt                                                                                 739                1,578
Deferred tax liability                                                                       9,277               10,451
Other liabilities                                                                            5,475                1,364
                                                                                          --------             --------
     Total liabilities                                                                     109,386               95,811
                                                                                          --------             --------

Stockholders' equity:
  Common stock, $.02 par value, 80,000,000 shares authorized,
  26,692,245 and 26,670,388 shares issued, respectively                                        534                  533
  Additional paid-in capital                                                               181,379              173,683
  Retained earnings                                                                         60,008               66,229
  Less treasury stock at cost, 1,917 and 57,895 shares, respectively                          (117)              (2,155)
                                                                                          --------             --------
     Total stockholders' equity                                                            241,804              238,290
                                                                                          --------             --------
     Total liabilities and stockholders' equity                                           $351,190             $334,101
                                                                                          ========             ========
</TABLE>




   The accompanying notes are an integral part of the condensed consolidated
                              financial statements.


                                       3
<PAGE>   4


                     THE BISYS GROUP, INC. AND SUBSIDIARIES
                 CONDENSED CONSOLIDATED STATEMENT OF OPERATIONS
                      (IN THOUSANDS, EXCEPT PER SHARE DATA)
                                   (UNAUDITED)


<TABLE>
<CAPTION>
                                                              Three Months Ended                 Six Months Ended
                                                                  December 31,                     December 31,
                                                           --------------------------      --------------------------
                                                             1998              1997          1998              1997
                                                           --------           -------      --------          --------
<S>                                                        <C>                <C>          <C>               <C>
Revenues                                                   $111,958           $91,431      $213,882          $182,893
                                                           --------           -------      --------          --------
Operating costs and expenses:
  Service and operating                                      63,895            53,671       123,767           107,889
  General and administrative                                 16,989            13,972        33,374            29,578
  Selling and conversion                                      6,079             4,378        11,118             8,534
  Research and development                                    2,935             2,854         6,116             5,725
  Amortization of intangible assets                           1,952               891         3,460             1,779
  Merger expenses and other charges                               -                 -           400            11,998
  Acquired in-process research and development                    -                 -        19,000                 -
                                                           --------           -------      --------          --------
Operating earnings                                           20,108            15,665        16,647            17,390
Interest income, net                                            243             1,025         1,040             2,050
                                                           --------           -------      --------          --------
Income before income taxes                                   20,351            16,690        17,687            19,440
Income taxes                                                  8,142             6,676        14,677             7,803
                                                           --------           -------      --------          --------
Net income                                                 $ 12,209           $10,014      $  3,010          $ 11,637
                                                           ========           =======      ========          ========

Basic earnings per share                                   $   0.46           $  0.38      $   0.11          $   0.44
                                                           ========           =======      ========          ========

Diluted earnings per share                                 $   0.44           $  0.37      $   0.11          $   0.43
                                                           ========           =======      ========          ========
</TABLE>


   The accompanying notes are an integral part of the condensed consolidated
                              financial statements.


                                       4
<PAGE>   5


                     THE BISYS GROUP, INC. AND SUBSIDIARIES
                 CONDENSED CONSOLIDATED STATEMENT OF CASH FLOWS
                                 (IN THOUSANDS)
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                                                               Six Months Ended
                                                                                                  December 31,
                                                                                         -----------------------------
                                                                                           1998                 1997
                                                                                         --------             --------
<S>                                                                                      <C>                  <C>
Cash flows from operating activities:
Net income                                                                               $  3,010             $ 11,637
Adjustments to reconcile net income to net cash provided
  by operating activities:
  Depreciation and amortization                                                            10,601                7,049
  Write-off of acquired in-process research and development                                19,000                    -
  Deferred income tax provision                                                               778                2,327
  Change in operating assets and liabilities, net of effects from acquisitions            (32,226)               7,924
                                                                                         --------             --------
Net cash provided by operating activities                                                   1,163               28,937
                                                                                         --------             --------

Cash flows from investing activities:
  Acquisition of businesses                                                               (20,340)                   -
  Net cash acquired in acquisitions                                                         4,554                1,490
  Capital expenditures, net                                                               (13,710)              (8,705)
  Proceeds from sales of investments                                                            -                1,203
  Purchase of investments                                                                  (2,899)              (6,513)
  Purchase of intangible assets                                                              (187)              (1,383)
  Other                                                                                       264                  301
                                                                                         --------             --------
Net cash used in investing activities                                                     (32,318)             (13,607)
                                                                                         --------             --------

Cash flows from financing activities:
  Proceeds from short-term borrowings                                                      20,000                    -
  Repayment of debt                                                                          (275)              (2,080)
  Proceeds from exercise of stock options                                                   5,938                3,017
  Repurchases of common stock                                                             (50,968)                   -
                                                                                         --------             --------
Net cash provided by (used in) financing activities                                       (25,305)                 937
                                                                                         --------             --------

Net increase (decrease) in cash and cash equivalents                                      (56,460)              16,267

Cash and cash equivalents at beginning of period                                           93,403               79,951
                                                                                         --------             --------

Cash and cash equivalents at end of period                                               $ 36,943             $ 96,218
                                                                                         ========             ========
</TABLE>



   The accompanying notes are an integral part of the condensed consolidated
                              financial statements.



                                       5
<PAGE>   6


                     THE BISYS GROUP, INC. AND SUBSIDIARIES
              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
                                   (UNAUDITED)

1.       THE COMPANY

         The BISYS(R) Group, Inc. and subsidiaries (the "Company") is a leading
         national provider of outsourcing solutions to and through financial
         organizations.

         The condensed consolidated financial statements include the accounts of
         The BISYS Group, Inc. and its subsidiaries and have been prepared
         consistent with the accounting policies reflected in the 1998 Annual
         Report on Form 10-K filed with the Securities and Exchange Commission
         and should be read in conjunction therewith. The condensed consolidated
         financial statements include all adjustments (consisting only of normal
         recurring adjustments) which are, in the opinion of management,
         necessary to present fairly this information.

2.       USE OF ESTIMATES

         The preparation of financial statements in conformity with generally
         accepted accounting principles requires management to make certain
         estimates and assumptions that affect the reported amounts of assets
         and liabilities and disclosure of contingent assets and liabilities at
         the date of the financial statements and the reported amounts of
         revenue and expenses during the reporting period. The most significant
         estimates are related to the allowance for doubtful accounts,
         intangible assets, merger expenses and other charges, acquired
         in-process research and development, income taxes and contingencies.
         Actual results could differ from these estimates in the near term.

3.       EARNINGS PER SHARE

         Basic and diluted EPS computations for the three and six months ended
         December 31, 1998 and 1997 are as follows (in thousands, except per
         share amounts):

<TABLE>
<CAPTION>
                                                              Three Months Ended                Six Months Ended
                                                                  December 31,                     December 31,
                                                             ----------------------          -----------------------
                                                              1998           1997             1998            1997
                                                             -------        -------          -------         -------
<S>                                                          <C>            <C>              <C>             <C>
         Basic EPS
         ---------
         Net income                                          $12,209        $10,014          $ 3,010         $11,637
                                                             =======        =======          =======         =======

         Weighted average common shares outstanding           26,643         26,199           26,497          26,156
                                                             =======        =======          =======         =======

         Basic earnings per share                            $  0.46        $  0.38          $  0.11         $  0.44
                                                             =======        =======          =======         =======


<CAPTION>
                                                              Three Months Ended                Six Months Ended
                                                                  December 31,                     December 31,
                                                             ----------------------          -----------------------
                                                              1998           1997             1998            1997
                                                             -------        -------          -------         -------
<S>                                                          <C>            <C>              <C>             <C>
         Diluted EPS
         -----------
         Net income                                          $12,209        $10,014          $ 3,010         $11,637
                                                             =======        =======          =======         =======

         Weighted average common shares outstanding           26,643         26,199           26,497          26,156

         Assumed conversion of common shares issuable
         under stock option plans                              1,218            941            1,078           1,044
                                                             -------        -------          -------         -------

         Weighted average common and common equivalent
         shares outstanding                                   27,861         27,140           27,575          27,200
                                                             =======        =======          =======         =======

         Diluted earnings per share                          $  0.44        $  0.37          $  0.11         $  0.43
                                                             =======        =======          =======         =======
</TABLE>



                                       6
<PAGE>   7


         Certain stock options were not included in the computation of diluted
         EPS because the options' exercise price was greater than the average
         market price of common shares during the period, as follows (in
         thousands, except per share amounts):

<TABLE>
<CAPTION>
                                                Three Months Ended                        Six Months Ended
                                                   December 31,                             December 31,
                                         ---------------------------------       ------------------------------------
                                              1998             1997                   1998                1997
                                              ----             ----                   ----                ----
<S>                                          <C>          <C>                    <C>                <C>
        Number of options excluded             91              1,650                   532                1,348

        Option price per share               $48.00       $32.25 to $39.00       $44.50 to $48.00    $34.00 to $39.00
</TABLE>


4.       BUSINESS COMBINATIONS

         On July 16, 1998, the Company completed its acquisition of Corelink
         Resources, Inc. (Corelink), which the Company has held a minority
         interest in since fiscal 1995. On August 10, 1998, the Company acquired
         Potomac Insurance Marketing Group, Inc. (Potomac). Both transactions
         have been accounted for by the purchase method of accounting and
         involved total cash consideration of $20.3 million. The operations of
         both Corelink and Potomac are included in the consolidated results of
         operations from the dates of acquisition. Pro forma information has not
         been presented due to lack of materiality.

         On September 16, 1998, the Company completed its acquisition of
         Greenway Corporation (Greenway) through the issuance of 968,202 shares
         of BISYS common stock held in treasury and issuance of 148,795
         equivalent stock options for all of the outstanding shares and stock
         options of Greenway. The acquisition, valued at approximately $43.8
         million, was treated as a purchase for accounting purposes, and,
         accordingly, the assets and liabilities were recorded based on their
         fair values at the date of the acquisition. Of the total purchase
         price, $15.6 million was allocated to goodwill, $7.4 million to other
         identifiable intangible assets, and $1.8 million to net tangible
         assets. In addition, $19.0 million was allocated to acquired in-process
         research and development, which was charged to operations at the time
         of the acquisition. Greenway's operations are included in the
         consolidated results of operations from the date of the acquisition.
         Pro forma information has not been presented due to lack of
         materiality.


                                       7
<PAGE>   8


ITEM 2.              MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  RESULTS OF OPERATIONS AND FINANCIAL CONDITION

The Company provides outsourcing solutions to and through financial
organizations which is reported as a single segment. The following table
presents the percentage of revenues represented by each item in the Company's
condensed consolidated statement of operations for the periods indicated:

<TABLE>
<CAPTION>
                                                             Three Months Ended                      Six Months Ended
                                                                December 31,                            December 31,
                                                           ----------------------                 ------------------------
                                                           1998             1997                  1998               1997
                                                           -----            -----                 -----              -----
<S>                                                        <C>              <C>                   <C>                <C>
Revenues                                                   100.0%           100.0%                100.0%             100.0%
                                                           -----            -----                 -----              -----

Operating costs and expenses:
  Service and operating                                     57.1             58.7                  57.9               59.0
  General and administrative                                15.2             15.3                  15.6               16.2
  Selling and conversion                                     5.4              4.8                   5.2                4.7
  Research and development                                   2.6              3.1                   2.8                3.1
  Amortization of intangible assets                          1.7              1.0                   1.6                1.0
  Merger expenses and other charges                            -                -                   0.2                6.5
  Acquired in-process research and development                 -                -                   8.9                  -
                                                           -----            -----                 -----              -----
Operating earnings                                          18.0             17.1                   7.8                9.5
Interest income                                              0.2              1.1                   0.5                1.1
                                                           -----            -----                 -----              -----
Income before income taxes                                  18.2             18.2                   8.3               10.6
Income taxes                                                 7.3              7.3                   6.9                4.3
                                                           -----            -----                 -----              -----
Net income                                                  10.9%            10.9%                  1.4%               6.3%
                                                           =====            =====                 =====              =====
</TABLE>

COMPARISON OF THE THREE MONTHS ENDED DECEMBER 31, 1998 WITH THE THREE MONTHS
ENDED DECEMBER 31, 1997.

        Revenues increased 22.5% from $91.4 million for the three months ended
        December 31, 1997 to $112.0 million for the three months ended December
        31, 1998. This growth was derived from sales to new clients, existing
        client growth, cross sales to existing clients and revenues from
        acquired businesses, partially offset by lost business.

        Service and operating expenses increased 19.1% from $53.7 million during
        the three months ended December 31, 1997 to $63.9 million for the three
        months ended December 31, 1998, and decreased as a percentage of
        revenues from 58.7% to 57.1%. The dollar increase resulted from
        additional costs associated with greater revenues.

        General and administrative expenses increased 21.6% from $14.0 million
        during the three months ended December 31, 1997, to $17.0 million for
        the three months ended December 31, 1998, and decreased as a percentage
        of revenues from 15.3% to 15.2%. The dollar increase primarily resulted
        from additional costs associated with recent acquisitions.

        Interest income was $0.8 million less for the three months ended
        December 31, 1998 compared to the same period last year due to the lower
        levels of invested cash and cash equivalents and higher interest expense
        associated with short-term borrowings.

        The income tax provision of $8.1 million for the three months ended
        December 31, 1998 increased from $6.7 million for the three months ended
        December 31, 1997 primarily due to higher taxable income. The provision
        represents an effective tax rate of 40% for both periods.

COMPARISON OF THE SIX MONTHS ENDED DECEMBER 31, 1998 WITH THE SIX MONTHS ENDED
DECEMBER 31, 1997.

        Revenues increased 16.9% from $182.9 million for the six months ended
        December 31, 1997 to $213.9 million for the six months ended December
        31, 1998. This growth was derived from sales to new clients, existing
        client growth, cross sales to existing clients and revenues from
        acquired businesses, partially offset by lost business.

        Service and operating expenses increased 14.7% from $107.9 million
        during the six months ended December 31, 1997 to $123.8 million for the
        six months ended December 31, 1998, and decreased as a percentage of




                                       8
<PAGE>   9

        revenues from 59.0% to 57.9%. The dollar increase resulted from
        additional costs associated with greater revenues.

        General and administrative expenses increased 12.8% from $29.6 million
        during the six months ended December 31, 1997, to $33.4 million for the
        six months ended December 31, 1998, and decreased as a percentage of
        revenues from 16.2% to 15.6%. The dollar increase primarily resulted
        from additional costs associated with recent acquisitions. The decrease
        as a percentage of revenues resulted from further utilization of
        existing general and administrative support resources.

        During the six months ended December 31, 1998, the Company wrote off
        $19.0 million of acquired in-process research and development associated
        with the acquisition of Greenway and incurred $0.4 million of
        merger-related expenses.

        The income tax provision of $14.7 million for the six months ended
        December 31, 1998 increased from $7.8 million for the six months ended
        December 31, 1997 primarily due to higher taxable income. The provision
        represents an effective tax rate of 40% for both periods, excluding the
        nonrecurring nondeductible charge of $19.0 million related to acquired
        in-process research and development incurred during the six months ended
        December 31, 1998.

LIQUIDITY AND CAPITAL RESOURCES

         At December 31, 1998, the Company had cash and cash equivalents of
         $36.9 million and working capital of approximately $43.3 million. At
         December 31, 1998, the Company had outstanding borrowings of $20.0
         million against its revolving credit facility to support working
         capital requirements. The credit facility bears interest at LIBOR plus
         a margin not to exceed 1.25%, or 6.22% at December 31, 1998. At
         December 31, 1998, the Company had $0.6 million outstanding in the form
         of letters of credit. The weighted average interest rate on other
         outstanding long-term borrowings of $0.8 million at December 31, 1998
         was 8.79%.

         For the six months ended December 31, 1998, operating activities
         provided cash of $1.2 million. Changes in operating assets and
         liabilities utilized cash of $32.2 million as a result of increases in
         accounts receivable due to revenue growth and reduction in accrued
         liabilities due largely to payments associated with client marketing
         programs that are administered by the Company's Fund Services division.
         The Company expects cash flow from operations to increase in the second
         half of fiscal year 1999. Investing activities used cash of $32.3
         million primarily for the acquisition of businesses of $20.3 million
         and capital expenditures of $13.7 million offset by cash acquired in
         acquisitions of $4.6 million. Financing activities used cash of $25.3
         million primarily for the repurchase of common stock of $51.0 million
         offset by borrowings of $20.0 million and $5.9 million of proceeds from
         the exercise of stock options.

         In accordance with the Company's stock buy-back program, the Company
         purchased approximately 1.2 million shares of its common stock for
         approximately $51.0 million in order to effect the acquisition of
         Greenway and for issuance of stock in connection with the exercise of
         stock options.

         In January 1999, the Company's Board of Directors authorized a new
         stock buy-back program of up to $100 million of its outstanding common
         stock. Purchases will occur from time-to-time in the open market to
         offset the possible dilutive effect of shares to be issued under
         employee benefit plans, for possible use in future acquisitions and for
         general and other corporate purposes. This new program supercedes and
         replaces the share repurchase program previously authorized by the
         Board of Directors.

MERGER EXPENSES AND OTHER CHARGES

         At December 31, 1998, approximately $1.2 million of costs to integrate
         new operations arising from prior acquisitions and costs relating to
         the realignment of certain operations are included in accrued
         liabilities on the accompanying balance sheet. Approximately $0.9
         million of such expenses were paid or charged against the related
         accruals during the three months ended December 31, 1998.

ACQUIRED IN-PROCESS RESEARCH AND DEVELOPMENT

         In September 1998, the Company acquired Greenway Corporation (Greenway)
         through the issuance of common stock valued at approximately $43.8
         million. Of the total purchase price, $19.0 million was allocated to
         acquired in-process research and development, which was charged to
         operations at the time of acquisition.



                                       9
<PAGE>   10

         The amount allocated to acquired in-process research and development
         was based on an independent appraisal, employing a discounted cash flow
         approach, and relates to the development of 32-bit and 32-bit enhanced
         products for the Company's check imaging software. At the acquisition
         date, the 32-bit product was estimated to be 75% complete and valued at
         $8.7 million, while the 32-bit enhanced product was estimated to be 50%
         complete and valued at $10.3 million.

         Significant assumptions used in the valuation of the acquired
         in-process research and development were as follows:

                 Estimated costs to complete           $2.1 million
                 Anticipated completion  date          January 2000
                 Projected annual revenues             $30 million
                 Discount rate                             20%
                 Discount period                         9 years

         Currently, the development efforts are proceeding ahead of schedule,
         and it is anticipated that technological feasibility of the products
         will be attained in the fiscal third quarter and development efforts
         completed by the end of the fiscal year.

         Research and development expenditures related to this product
         development effort approximated $375,000 for the three months ended
         December 31, 1998, and are included in the consolidated statement of
         operations.

YEAR 2000

         The Company is addressing the Year 2000 issues associated with its
         existing computer systems and software applications utilizing both
         internal and external resources to identify and remediate these matters
         throughout the organization. The Company has completed its risk
         assessment and testing plans for internal mission critical information
         systems and continues to remediate other systems that are not currently
         Year 2000 ready. The Company anticipates that all of its internal
         mission critical information systems will be tested and Year 2000 ready
         by March 31, 1999. In the event such systems are not Year 2000 ready by
         December 31, 1999, it could have a material adverse impact on the
         Company's business and results of operations.

         The Company uses third party provided software and systems in certain
         of its businesses for such tasks as account and information statement
         processing, fund accounting, and 401(k) plan record keeping. If third
         parties upon which the Company depends, including telecommunications
         and electrical power providers, are unable to address their Year 2000
         issues in a timely manner, it could result in a material adverse
         financial risk to the Company. In order to minimize this risk, the
         Company is devoting resources necessary to develop appropriate business
         continuity plans. These contingency plans will include alternative
         systems and vendors, disaster recovery hot sites, alternative power
         sources, and manual processes. These contingency plans are expected to
         be completed prior to June 30, 1999.

         The Company's Year 2000 progress, the testing of remediated software,
         and contingency plans have been and will continue to be the subject of
         independent verification and validation by the Company's Internal Audit
         function. Internal Audit reports on Year 2000 are reviewed by senior
         management and the Company's Board of Directors.

         The Company believes it has developed an effective plan to address the
         Year 2000 issues and that, based on available information, its Year
         2000 transition will not have a material effect on its business,
         operations, or financial results. The Company anticipates expenditures
         for Year 2000 testing and remediation in the range of $3.0 to $4.0
         million in fiscal 1999 and less than $1.5 million in the first half of
         fiscal 2000. During the six months ended December 31, 1998, the Company
         incurred Year 2000 expenditures of $1.3 million.

SAFE HARBOR STATEMENT UNDER THE PRIVATE SECURITIES LITIGATION REFORM ACT OF 1995

         Except for the historical information contained herein, the matters
         discussed in this quarterly report are forward-looking statements which
         involve risks and uncertainties, including but not limited to economic,
         competitive, governmental and technological factors affecting the
         Company's operations, markets, services and related products, prices,
         and other factors discussed in the Company's prior filings with the
         Securities and Exchange Commission. Although the Company believes that
         the assumptions underlying the forward-looking



                                       10
<PAGE>   11

         statements contained herein are reasonable, any of the assumptions
         could be inaccurate. Therefore, there can be no assurance that the
         forward-looking statements included in this quarterly report will prove
         to be accurate. In light of the significant uncertainties inherent in
         the forward-looking statements included herein, the inclusion of such
         information should not be regarded as a representation by the Company
         or any other person that the objectives and plans of the Company will
         be achieved.



                                       11
<PAGE>   12


                                                      PART II

ITEM 4.           SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

                  At the Annual Meeting of Stockholders of the Company, held on
                  November 16, 1998, the Stockholders approved the following
                  matters:

                  1.       Re-election of all six Directors named below to hold
                           office until the next Annual Meeting of Stockholders
                           and until their successors have been duly elected and
                           qualified:

<TABLE>
<CAPTION>
                                                                                                 Number of
                           Name of Director                                                    Votes in Favor
                           ----------------                                                    --------------
                           <S>                                                                 <C>
                           Robert J. Casale                                                      22,006,495
                           Thomas A. Cooper                                                      22,006,340
                           Jay W. DeDapper                                                       22,005,180
                           John J. Lyons                                                         22,006,715
                           Lynn J. Mangum                                                        22,006,933
                           Thomas E. McInerney                                                   22,006,915


<CAPTION>
                                                                                  For           Against       Abstain
                                                                                  ---           -------       -------
                  <S>                                                          <C>              <C>           <C>
                  2.       1999 Employee Stock
                           Purchase Plan                                       21,837,673       176,221        52,919

                  3.       Appointment of PricewaterhouseCoopers LLP
                           as independent accountants for
                           fiscal year 1999                                    22,060,037        3,969          2,807
</TABLE>



ITEM 6.           EXHIBITS AND REPORTS ON FORM 8-K

         (a)      EXHIBITS

                  None.

         (b       REPORTS ON FORM 8-K

                  None.


                                       12
<PAGE>   13


                                   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.


                                                THE BISYS GROUP, INC.



Date: February 11, 1999                         By: /s/ Dennis R. Sheehan
     ------------------                            -------------------------
                                                Dennis R. Sheehan
                                                Executive Vice President and
                                                Chief Financial Officer
                                                (Duly Authorized Officer)



                                       13
<PAGE>   14


                              THE BISYS GROUP, INC.
                                  EXHIBIT INDEX



EXHIBIT NO.                                                PAGE

         (27)     Financial Data Schedule..................(electronic only)



                                       14