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


                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20552

                             ----------------------

(MARK ONE)
[X]  QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE
     ACT OF 1934
     For the quarterly period ended SEPTEMBER 30, 1998


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

     For the transition period from                    to 
                                    ------------------    -------------------


                           COMMISSION FILE NO. 0-22499


                            BAYONNE BANCSHARES, INC.
             ------------------------------------------------------
             (Exact name of registrant as specified in its charter)

          Delaware                                            22-3511899
-------------------------------                          --------------------
(State or other jurisdiction of                           (I.R.S. Employer
incorporation or organization)                            Identification Number)

                     568 Broadway, Bayonne, New Jersey 07002
                    ----------------------------------------
                    (Address of principal executive offices)

       Registrant's telephone number, including area code: (201) 437-1000

--------------------------------------------------------------------------------

Former name, former address and former fiscal year, if changed since last report

     Indicate by check |X| 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 reports), and (2) has been subject to such
filing requirements for the past 90 days.

          Yes |X| No [ ]

            AS OF NOVEMBER 13, 1998, THERE WERE 9,139,507 SHARES OF THE
                      REGISTRANT'S COMMON STOCK OUTSTANDING


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


<PAGE>


                            BAYONNE BANCSHARES, INC.

                                      INDEX

PART I.     FINANCIAL INFORMATION                                          Page

Item 1.     Consolidated Financial Statements

            Consolidated Statements of Financial Condition as of           1
            September 30, 1998 and March 31, 1998

            Consolidated Statements of Income for the three and six        2
            months ended September 30, 1998 and 1997                        
           
            Consolidated Statements of Stockholders' Equity for the six    3
            months ended September 30, 1998 and 1997

            Consolidated Statements of Cash Flows for the six              4-5  
            months ended September 30, 1998 and 1997

            Notes to Consolidated Financial Statements                     6-7

Item 2.     Management's Discussion and Analysis of Financial              8-13
            Condition and Results of Operations

Item 3.     Quantitative and Qualitative Disclosures About Market Risk     14
                   
PART II.    OTHER INFORMATION                                              15


<PAGE>




PART I                       FINANCIAL INFORMATION
ITEM 1
                       Consolidated Financial Statements


<TABLE>
<CAPTION>
                                     BAYONNE BANCSHARES, INC.
                          CONSOLIDATED STATEMENTS OF FINANCIAL CONDITION
                                     (IN THOUSANDS OF DOLLARS)


                                                             September 30, 1998      March 31, 1998
                                                             --------------------------------------
                                                                (unaudited)
ASSETS
<S>                                                               <C>                  <C>
Cash and cash equivalents:
 Cash on hand and in banks                                        $   3,042            $   4,712
 Deposits with financial institutions                                  --                 11,900
 AMF short-term fund                                                      5                    5 
                                                                  ---------            ---------
  Total cash and cash equivalents                                     3,047               16,617


Securities available for sale, at market value                      324,457              362,778
Securities held to maturity                                          11,708               10,274
Loans receivable, net                                               308,789              235,465
Accrued interest receivable, net                                      3,901                4,089
Federal Home Loan Bank stock, at cost                                10,511                7,460
Real estate acquired in settlement of loans                             501                  330
Office properties and equipment, net                                  5,524                5,351
Prepaid expenses                                                        987                  672
Other assets                                                          3,232                3,022 
                                                                   --------             --------
 Total Assets                                                     $ 672,657            $ 646,058 
                                                                  =========            ========= 
                                                                 
LIABILITIES AND STOCKHOLDERS' EQUITY

                                                       
Liabilities:
 Deposits                                                         $ 420,749            $ 423,545
 Borrowings                                                         146,750              115,000
 ESOP loan                                                              272                  380
 Advance payment by borrowers for taxes and insurance                 3,969                3,754
 Accrued expenses and other liabilities                               5,765                4,730 
                                                                  ---------            ---------
  Total Liabilities                                               $ 577,505            $ 547,409 
                                                                  =========            ========= 

Stockholders' equity:
 Common stock                                                            91                   91
 Additional paid in capital                                          60,995               60,246
 Common stock acquired by ESOP and MRP                               (7,068)              (4,301)
 Retained earnings-substantially restricted                          44,999               43,702
 Accumulated comprehensive loss                                      (3,865)              (1,089)
                                                                  ---------            ---------
  Total stockholders' equity                                         95,152               98,649 
                                                                  ---------            --------- 
   Total liabilities and Stockholders' equity                     $ 672,657            $ 646,058 
                                                                  =========            ========= 
                 
</TABLE>
        See accompanying notes to the consolidated financial statements.

                                       1


<PAGE>


<TABLE>
<CAPTION>    
                                          BAYONNE BANCSHARES, INC. AND SUBSIDIARIES
                                             CONSOLIDATED STATEMENTS OF INCOME
                                                 (IN THOUSANDS OF DOLLARS)
                                                        (UNAUDITED)


                                                                    Three Months                       Six Months
                                                                 Ended September 30,               Ended September 30,
                                                                --------------------           ---------------------------
                                                                  1998        1997               1998               1997
                                                                --------    --------           --------           -------- 
<S>                                                             <C>         <C>                <C>                <C>
Interest and dividend income:
 Loans                                                          $  6,088    $  4,884           $ 11,007           $  9,801
 Securities available for sale                                     4,590       4,988              9,937              9,571
 Securities held to maturity                                         381         297                704                602
 Overnight deposits with financial institutions                       78         124                136                212 
                                                                --------    --------           --------           -------- 
Total interest and dividend income                              $ 11,137    $ 10,293           $ 21,784           $ 20,186 
                                                                --------    --------           --------           -------- 

Interest expense:
 Interest on deposits                                              4,561       5,191              9,153             10,377
 Interest on other borrowings                                      2,174       1,238              3,989              2,368 
                                                                --------    --------           --------           -------- 
  Total interest expense                                           6,735       6,429             13,142             12,745 
                                                                --------    --------           --------           -------- 

Net interest income                                                4,402       3,864              8,642              7,441
 Provision for loan losses                                            75          45                125                 90 
                                                                --------    --------           --------           -------- 
Net interest income after  provision for loan losses               4,327       3,819              8,517              7,351 
                                                                --------    --------           --------           -------- 
 
Other Income
 Loan fees and service charges                                        69          63                137                131
 Deposit fees                                                        159         147                318                278
 Gain (loss) on securities available for sale, net                   197          (5)               176                 (5)
 Income from Subsidiary                                               69          26                115                 73
 (Loss) gain on sales of real estate acquired in
  settlement of loans, net                                            (8)         (1)               (22)                11
 Other                                                                52          53                125                194 
                                                                --------    --------           --------           -------- 
  Total other income                                                 538         283                849                682 
                                                                --------    --------           --------           -------- 

Operating expenses:
 Compensation and employee benefits                                1,589       1,476              3,164              2,942
 Occupancy and equipment                                             310         311                620                602
 Data processing service expense                                     210         207                421                431
 Deposit insurance premiums                                          135         142                272                287
 Other                                                               524         428              1,024                902 
                                                                --------    --------           --------           -------- 
  Total operating expenses                                         2,768       2,564              5,501              5,164 
                                                                --------    --------           --------           -------- 


Income before income tax expense                                   2,097       1,538              3,865              2,869
Income tax expense                                                   776         569              1,430              1,062 
                                                                --------    --------           --------           -------- 
Net income                                                      $  1,321    $    969           $  2,435           $  1,807 
                                                                ========    ========           ========           ======== 
Basic earnings per share                                        $   0.15    $   0.11           $   0.27           $   0.20 
                                                                ========    ========           ========           ======== 
Diluted earnings per share                                      $   0.15    $   0.11           $   0.27           $   0.20 
                                                                ========    ========           ========           ======== 

</TABLE>


        See accompanying notes to the consolidated financial statements.

                                        2


<PAGE>


<TABLE>
<CAPTION>
                                                    BAYONNE BANCSHARES, INC.
                                                        AND SUBSIDIARIES
                                          CONSOLIDATED STATEMENTS OF STOCKHOLDERS' EQUITY
                                        SIX MONTH PERIODS ENDED SEPTEMBER 30, 1998 AND 1997
                                                     (IN THOUSANDS OF DOLLARS)
                                                            (UNAUDITED)


                                                                                        Retained
                                                Additional   Unallocated Unamortized    Earnings        Accumulated       Total
                                      Common     Paid in        ESOP        MRP        Substantially   Comprehensive   Stockholders'
                                      Stock      Capital       Shares      Shares       Restricted          Loss          Equity
------------------------------------------------------------------------------------------------------------------------------------

<S>                                   <C>       <C>           <C>        <C>            <C>               <C>           <C>
Balance at March 31, 1997             $  90     $ 12,643      $   (598)  $   (378)      $ 40,658          $ (4,336)     $ 48,079
Net income for the six month 
 period ended September 30, 1997       --           --            --         --            1,807              --           1,807
Amortization of ESOP                   --             57           109       --             --                --             166
Amortization of MRP                    --             22          --           81           --                --             103
Dividend Paid                          --           --            --         --             (528)             --            (528)
Exercise of stock options              --             61          --         --             --                --              61
Comprehensive income                                                                                         2,902         2,902
Establishment of second ESOP           --           --          (3,895)      --             --                --          (3,895)
Issuance and exchange of
 common stock as a result
 of the conversion/reorganization      --         46,466          --         --             --                --          46,466
                                      -----     --------      --------    -------       --------          --------      --------
Balance at September 30, 1997         $  90     $ 59,249      $ (4,384)   $  (297)      $ 41,937          $ (1,434)     $ 95,161
                                      =====     ========      ========    =======       ========          ========      ========
                                       
Balance at March 31, 1998             $  91     $ 60,246      $ (4,081)    $ (220)      $ 43,702          $ (1,089)     $ 98,649
Net income for the six month 
 period ended September 30, 1998       --           --            --         --            2,435              --           2,435
Amortization of ESOP                   --            465           239       --             --                --             704
Amortization of MRP                    --            130          --          249           --                --             379
Dividend Paid                          --           --            --         --           (1,138)             --          (1,138)
Exercise of stock options              --            154          --         --             --                --             154
Purchase of shares for MRP Plan                                            (3,255)                                        (3,255)
Comprehensive loss                     --           --            --         --             --              (2,776)       (2,776)
                                       -----     --------      --------    -------       --------          --------      --------   
 Balance at September 30, 1998         $  91     $ 60,995      $ (3,842)   $(3,226)      $ 44,999          $ (3,865)     $ 95,152
                                       =====     ========      ========    =======       ========          ========      ========
</TABLE>


          See accompanying notes to consolidated financial statements.

                                       3


<PAGE>


<TABLE>
<CAPTION>

                                    BAYONNE BANCSHARES, INC. AND SUBSIDIARIES
                                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                                            (IN THOUSANDS OF DOLLARS)
                                                   (UNAUDITED)

                                                                                Six Months Ended September 30,
                                                                            ------------------------------------
                                                                               1998                       1997
                                                                            ---------                  ---------
<S>                                                                         <C>                        <C>
Cash flows from operating activities:
Net income                                                                  $   2,435                  $   1,807

Adjustments to reconcile net income to net cash provided by
 (used in) operating activities:

 Depreciation of office properties and equipment                                  298                        284
 (Gain) loss on securities available for sale                                    (176)                         5
 Provision for loan losses                                                        125                         90
 Loss (gain) on real estate operations                                             22                        (11)
 Amortization of premiums on
  investment securities and mortgage backed securities                          1,271                        240
 Amortization of ESOP and MRP shares                                            1,083                        469
 Net increase in deferred loan fees                                              (123)                       (91)
 Net increase (decrease) in accrued interest receivable                           188                       (205)
 Net (decrease) increase in prepaid expenses                                     (315)                       542
 Net (decrease) increase in other assets                                         (210)                       678
 Net increase (decrease) in accrued expenses and other liabilities              1,108                     (3,191)
                                                                            ---------                  ---------   
  Total adjustments                                                             3,271                     (1,190)
                                                                            ---------                  ---------    
  
  Net cash provided by operating activities                                     5,706                        617
                                                                            ---------                  ---------  

Cash flows from investing activities:

 Principal payments and maturities on securities available for sale         $  77,518                  $  24,521
 Proceeds from securities available for sale                                   87,654                       --
 Purchases of securities available for sale                                  (135,951)                   (61,076)
 Net (increase) decrease in loans receivable                                  (73,449)                     3,394
 Maturities of securities held to maturity                                      3,554                        984
 Proceeds from sales of real estate acquired in settlement of loans                25                        276
 Purchase of FHLB stock                                                        (3,051)                      --
 Purchase of premises and equipment                                              (398)                       (28)
                                                                            ---------                  ---------
  Net cash used in investing activities                                        44,098                     31,929
                                                                            ---------                  ---------

Cash flows from financing activities:
 Net decrease in deposits                                                      (2,796)                  (12,008)
 Net increase in advance payments by borrowers for taxes and insurance            215                        274
 Dividends paid                                                                (1,138)                      (528)
 Increase in borrowings and repurchase agreements                              31,750                       --
 Payment on ESOP debt                                                            (108)                      (109)
 Issuance of common stock as a result of the conversion/reorganization           --                       42,371
 Exercise of stock options                                                        154                         61
                                                                            ---------                  ---------
  Net cash provided by financing activities                                 $  24,822                  $  30,061
                                                                            ---------                  ---------
</TABLE>                                                                     


        See accompanying notes to the consolidated financial statements

                                       4


<PAGE>


<TABLE>
<CAPTION>

                      BAYONNE BANCSHARES, INC. AND SUBSIDIARIES
                  CONSOLIDATED STATEMENTS OF CASH FLOWS, (CONTINUED)
                              (IN THOUSANDS OF DOLLARS)
                                      (UNAUDITED


                                                       Six Months Ended September 30,
                                                       ------------------------------
                                                           1998              1997
                                                         --------          --------

<S>                                                      <C>               <C>
Net decrease in cash and cash equivalents                $(13,570)         $ (1,251)

Cash and cash equivalents at start of period             $ 16,617          $ 15,472
                                                         --------          --------
                                                    
Cash and cash equivalents at end of period               $  3,047          $ 14,221
                                                         ========          ========
                           

Supplemental schedule of cash flow information:

Real estate acquired in settlement of loans              $    190          $    302
Taxes Paid                                               $    956          $    769
Interest Paid                                            $ 13,127          $ 12,745
</TABLE>


        See accompanying notes to the consolidated financial statements.

                                       5


<PAGE>


                    BAYONNE BANCSHARES, INC. AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS


1)   BASIS OF PRESENTATION

     The accompanying unaudited consolidated financial statements have been
prepared in accordance with generally accepted accounting principles for interim
financial information and in conformity with the instructions to Form 10-Q and
Article 10 of Regulation S-X for Bayonne Bancshares, Inc. (the `Company") and
Subsidiaries. The Company is the holding company of First Savings Bank of New
Jersey, SLA, a New Jersey chartered savings and loan association (the "Bank").


2)   CONVERSION AND REORGANIZATION

     On August 22, 1997, Bayonne Bancshares, Inc. in accordance with the Bank's
plan of conversion and reorganization sold 4,869,190 shares of common stock at a
price per share of $10.00. In addition, each of the 1,410,735 shares of common
stock of First Savings Bank of New Jersey, SLA held by public stockholders were
exchanged for 2.933 shares of common stock of Bayonne Bancshares, Inc. in
accordance with the Bank's Plan of Conversion and Agreement and Plan of
Reorganization.


3)   NON-PERFORMING LOANS

     Non-performing loans at September 30, 1998, and March 31, 1998 are as
follows (in thousands of dollars):


<TABLE>
<CAPTION>
                                                   September 30, 1998         March 31, 1998
                                                   ------------------         --------------
<S>                                                      <C>                      <C>
Loans delinquent 90 days or more
and other non-performing loans                           $4,284                   $3,817
                                                         ------                   ------

Loans delinquent 90 days or more and
other non-performing loans as a
percentage of  loans receivable, net                      1.39%                    1.62%
</TABLE>


     An analysis of the allowance for loan losses for the six-month periods
ended September 30, 1998 and 1997 is as follows (in thousands of dollars)


                                    September 30, 1998       September 30, 1997
                                    ------------------       ------------------
Balance at start of period               $2,953                    $3,158      
Provision charged to operations             125                        90
Net (charge-offs) recoveries                (43)                     --
                                         ------                    ------
Balance at end of period                 $3,035                    $3,248
                                         ======                    ======


                                       6


<PAGE>


4)   EARNINGS PER SHARE


     The Bank adopted SFAS No. 128, "Earnings Per Share," on December 31, 1997.
SFAS No. 128 established the new standard for computation and presentation of
net income per common share. Under the new requirements both basic and diluted
net income per common share are presented. All prior period net income per
common share data has been restated.

     Basic net income per common share is calculated by dividing net income,
less the dividends on preferred stock, if any, by the average common shares
outstanding during the period.

     Diluted net income per common share is calculated similar to that of the
basic net income per common share except that the denominator is increased to
include the number of additional common shares that would have been outstanding
if all potentially dilutive common shares arising from unexercised stock options
were issued during the reporting period.

     As discussed in note 2, the Company completed a conversion and
reorganization, which included the exchange of previously outstanding shares for
new shares of the stock holding company, Bayonne Bancshares, Inc., at an
exchange ratio of 2.933 to 1. All historical share and per share information has
been adjusted to reflect this change unless otherwise noted.

     The following table summarizes the computation of basic earnings and
diluted earnings per common share for the three and six months ended September
30, 1998 and 1997:

<TABLE>
<CAPTION>
                                                   Three months ended          Six months ended
                                                      September 30               September 30
                                                -----------------------     -----------------------
(Dollars in thousands, except per share data)      1998         1997           1998         1997
                                                ----------   ----------     ---------    ----------
                                                                           
<S>                                             <C>          <C>            <C>          <C>        
Earnings available to common shareholders       $    1,321   $      969     $    2,435   $    1,807
                                                ==========   ==========     ==========   ==========
                                                                           
Weighted average common shares outstanding       9,041,000    8,640,527      9,022,484    8,907,145
                                                                           
Plus common stock equivalents                      133,637       14,950        133,637       54,490
                                                ----------   ----------     ----------   ----------
Diluted weighted average shares outstanding      9,174,637      8,655,477    9,156,121    8,961,635
                                                ==========   ==========     ==========   ==========
                                                                           
Earnings per common share:                                                 
                                                                           
Basic                                           $     0.15   $     0.11     $     0.27   $     0.20
                                                ==========   ==========     ==========   ==========
                                                                           
Diluted                                         $     0.15   $     0.11     $     0.27   $     0.20
                                                ==========   ==========     ==========   ==========
</TABLE>


                                       7


<PAGE>


5)   RECLASSIFCATIONS

     Certain reclassifications have been made to the 1997 amounts to conform to
the 1998 presentation.


6)   PROPOSED MERGER WITH RICHMOND COUNTY FINANCIAL CORP.

     The Company announced on July 20, 1998 that it had entered into a
definitive agreement to merge with Richmond County Financial Corp., which
agreement was amended and restated on October 14, 1998. Under the terms of the
agreement, which is subject to approval by shareholders of each company and
regulatory authorities, the Company's shareholders will receive 1.05 shares of
Richmond County Financial Corp. common stock for each share of the Company
owned. The transaction is intended to be a tax-free merger accounted for as a
purchase transaction and is expected to be completed by the first quarter of
calendar 1999. The Amended and Restated Agreement and Plan of Merger was
included as an exhibit to the Form 8-K filed by the Company on October 16, 1998.


7)   RECENT ACCOUNTING PRONOUNCEMENT

     In June 1998, the Financial Accounting Standards Board issued SFAS No. 133,
"Accounting for Derivative Instruments and Hedging Activities." This statement
establishes accounting and reporting standards for derivative instruments, and
for hedging activities. This statement is effective for periods commencing
January 1, 2000. The Company is currently evaluating the impact this statement
will have on its results of operations and its financial position. The effect of
adopting this statement is not expected to have a material effect on the
Company's results of operations or financial condition.


8)   COMPREHENSIVE INCOME

     During the quarter ended September 30, 1998, the Company adopted SFAS No.
130, "Reporting Comprehensive Income." SFAS No. 130 requires the reporting of
comprehensive income in addition to net income from operations. Comprehensive
income is a more inclusive financial reporting methodology that includes
disclosure of certain financial information that historically has not been
recognized in the calculation of net income. The financial statements reflect
the adoption of SFAS N0 130.

     Total comprehensive (loss) income for the six months ended September 30,
1998 and 1997 was $(341,000) and $1,095,000, respectively. For the six months
ended September 30, 1998, total comprehensive loss represented net income of
$2,435,000 and


                                       8


<PAGE>
                                    

other comprehensive loss of $2,776,000. For the six months ended September 30,
1997, total comprehensive loss represented net income of $1,807,000 and other
comprehensive income of $2,902,000. Other comprehensive income for the
above-mentioned periods related to unrealized gains/losses on securities
available for sale, net of tax.



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

FINANCIAL CONDITION

     Stockholders' equity decreased by $3.4 million to $95.2 million at
September 30, 1998 from $98.6 million at March 31, 1998. The decrease in
stockholders equity is attributable to the acquisition of 194,768 shares of
common stock for $3.3 million to be used for stock awards under the Bayonne
Bancshares, Inc. 1998 Stock Based Incentive Plan, and a $2.8 million of
comprehensive loss relating to the mark-to-market adjustment on securities
available for sale, partially offset by net income of $2.4 million for the six
months ended September 30, 1998. At September 30, 1998, the tangible, core
and risk based capital ratios were 12.24%, 12.24%, and 27.30%, respectively.

     Total assets increased by $26.6 million to $672.7 million at September 30,
1998 compared to $646.1 million at March 31, 1998. Securities available for
sale, at market value decreased by $ 38.3 million or 10.6% to $324.5 million at
September 30, 1998 from $362.8 million at March 31, 1998. The decrease was
primarily attributable to the sale of $45.0 million of US Government treasuries
and agencies and $12.0 million of mortgage backed securities, which was
partially offset by the purchase of $25.0 million of variable rate trust
preferred securities.

     Loans receivable, net, increased by $73.3 million or 31.1% to $ 308.8
million at September 30, 1998 compared to $235.5 million at March 31, 1998. The
increase primarily resulted from the purchase of $80.0 million of seasoned,
fixed rate single family loans yielding approximately 6.5%, with approximately
$58.0 million of these loans located in New Jersey, New York and Pennsylvania.
The increase in loans receivable, net, was partially reduced by net amortization
and payoffs of $18.8 million on mortgage loans during the quarter.

     Total liabilities increased by $30.1 million or 5.50% to $577.5 million as
of September 30, 1998 compared to $547.4 million at March 31, 1998. Borrowings
increased by $31.8 million or 27.6% to $146.8 million at September 30, 1998
compared to $115.0 million at March 31, 1998. Wholesale borrowings were used to
increase the Bank's holdings of variable-rate trust preferred and mortgage
backed securities, to fund a portion of the whole loan purchase and to fund the
outflow of maturing high yielding certificates of deposit.


                                       9


<PAGE>


RESULTS OF OPERATIONS FOR THE THREE MONTHS ENDED SEPTEMBER 30, 1998

     Net income was $1,321,000 for the three months ended September 30, 1998
compared to $969,000 for the quarter ended September 30, 1997. Total interest
and dividend income increased by $844,000 or 8.2% to $11.1 million for the three
months-ended September 30,1998 compared to $10.3 million for the comparable
prior year quarter. This increase primarily resulted from an increase in average
earning assets of $73.6 million to $662.0 million for the three months ended
September 30, 1998 compared to $588.4 million for the comparable period ending
September 30, 1997. The increase was partially offset by a decrease in the yield
on average interest earning assets to 6.73% for the three months ended September
30, 1998 from the 7.00% yield for the three months ended September 30, 1997. The
increase in average interest earning assets was primarily due to the $80.0
million in whole loans purchased on June 30, 1998. The interest income from
these loans approximated $1.4 million for the quarter ended September 30, 1998.

     Total interest expense increased by $306,000 to $6.7 million for the three
months ended September 30, 1998 compared to $6.4 million for the comparable
prior year quarter. The increase primarily resulted from an increase in average
interest bearing liabilities of $49.6 million or 9.4 % to $576.1 million for the
three months ended September 30, 1998 from $526.5 million for the three months
ended September 30, 1997. The increase in average interest bearing liabilities
was primarily due to an increase in average borrowings of $65.4 million or 73.7%
to $154.1 million for the three months ended September 30, 1998 compared to
$88.7 million for the comparable prior year quarter.

     The provision for loan losses totaled $75,000 and $45,000 for the
three-month period ended September 30, 1998 and 1997, respectively. The
provision is a result of management's judgement based on a review of the Bank's
loans and consideration of a variety of factors, including, but not limited to,
(1) the risk characteristics of the loan portfolio, (2) current economic
conditions, (3) actual losses previously experienced and (4) the existing levels
of reserve for possible losses in the future. Non-performing loans at September
30, 1998 and March 31, 1998 were $4.3 million and $3.8 million or 1.39% and
1.62% of loans receivable, net, respectively.

     Total other income increased by $255,000 to $538,000 for the three months
ended September 30, 1998 compared to $283,000 for the comparable prior year
quarter. The increase was primarily attributable to gains on sales of securities
available for sale of $197,000 during the quarter compared to a loss of $5,000
for the quarter ended September 30, 1997 and income from Bayonne Service Corp.,
which increased by $43,000 to $69,000 for the quarter ended September 30, 1998
compared to $26,000 for the quarter ended September 30, 1997. Bayonne Service
Corp. is a wholly owned subsidiary of the Bank engaged in the sale of
non-deposit investment products.


                                       10


<PAGE>


     Total operating expense increased by $204,000 or 8.0% to $2.8 million for
the three months ended September 30, 1998 compared to $2.6 million for the three
months ended September 30, 1997. Compensation and employee benefits increased by
$112,000 or 7.6% due to increased expenses from new and existing ESOP and
Management Recognition Plans of $280,000 which was partially offset by the lower
salary expense of $66,000.

     Income tax expense for the quarter increased by $207,000 to $776,000 for
the three months ended September 30, 1998 compared to $569,000 for the
comparable prior year quarter as a result of an increase of $559,000 in income
before income taxes for the three months ended September 30, 1998 compared to
the income before income taxes for the same prior year quarter.

RESULTS OF OPERATIONS FOR THE SIX MONTHS ENDED SEPTEMBER 30, 1998

     Net income increased by $628,000 or 34.8% to $2.4 million for the six
months ended September 30, 1998 compared to $1.8 million for the six months
ended September 30, 1997. This increase resulted from an increase in average
interest earning assets of $75.4 million to $651.8 million for the six months
ended September 30, 1998 from $576.3 million for the comparable prior year
period, which was partially offset by a decrease in yield on average interest
earning assets to 6.68% for the six months ended September 30, 1998 from the
7.01% for the six months ended September 30, 1997. The increase in average
interest earning assets was primarily due to the $80.0 million in whole loans
purchased on June 30, 1998. The interest income from these loans approximated
$1.4 million for the six months ended September 30, 1998.

     Total interest expense increased by $397,000 or 3.1% to $13.1 million for
the six months ended September 30, 1998 compared to $12.7 million for the
comparable prior year period. The increase primarily resulted from an increase
of $40.4 million or 7.7% in average interest bearing liabilities to $565.3
million for the six months ended September 30, 1998 compared to $524.9 million
for the six months ended September 30, 1997. This increase in average interest
bearing liabilities was primarily due to an increase in average borrowings of
$58.9 million to $143.2 million for the six months ended September 30, 1998
compared with $84.3 million for the comparable prior year period.

     The provision for loan losses totaled $125,000 and $90,000 for the
six-month periods ended September 30, 1998 and 1997, respectively. The provision
is the result of management's judgement based on a review of its loans and a
consideration of a variety of factors including, but not limited to, (1) the
risk characteristics of its loan portfolio, (2) current economic conditions, (3)
actual losses previously experienced and (4) the existing levels of reserve for
possible loan losses in the future. Non-performing loans at September 30, 1998
and March 31, 1998 were $4.3 million and $3.8 million or 1.39% and 1.62% of
loans receivable, net, respectively.


                                       11

<PAGE>


     Total other income increased by $167,000 or 24.5% to $849,000 for the six
months ended September 30, 1998 compared to $682,000 for the six months ended
September 30, 1997. The increase was primarily attributable to gains on sale of
securities available for sale of $176,000 for the six months ended September 30,
1998.

     Total operating expense increased by $337,000 or 6.5% to $5.5 million for
the six-month's ended September 30, 1998 from $5.2 million for the comparable
prior year period. This increase was primarily the result of an increase in
compensation and employee benefits of $221,000 or 7.5% due to increased expense
of $533,000 for new and existing ESOP and Management Recognition Plans to $1.1
million for the six months ended September 30, 1998 compared to $548,000 for the
six months ended September 30, 1997. The increase was partially offset by lower
executive salary and employee benefit expenses of $346,000 compared to the
comparable prior year period. Other operating expenses increased by $124,000 to
$1.0 million from $902,000 primarily due to the increase in shareholder services
expense of $111,000.

     Income tax expense increased to $1.4 million for the six months ended
September 30, 1998 from $1.1 million for the six months ended September 30, 1997
as a result of an increase of $996,000 in pre-tax income for the six-month
period ended September 30, 1998.



CAPITAL

     The OTS requires that the Bank meet minimum tangible, core and risk-based
capital requirements. As of September 30, 1998, the Bank exceeded all regulatory
capital requirements. The Bank's required, actual and excess capital levels as
of September 30, 1998 were as follows (in thousands of dollars):

<TABLE>
<CAPTION>    
                                                                                         Excess of Actual
                                    Required         % of      Actual          % of      Over Regulatory
                                     Amount         Assets     Amount         Assets       Requirements
                                    --------        ------     ------         ------     ----------------

<S>                                 <C>             <C>       <C>             <C>            <C>
Tangible Capital.........           $ 9,885         1.50%     $80,651         12.24%         $70,766
Core Capital.............           $26,361         4.00%     $80,651         12.24%         $54,290
Risk-based Capital.......           $23,635         8.00%     $80,651         27.30%         $57,016
</TABLE>

     If the allowance for marketable debt and equity securities was included in
capital, the Bank's tangible, core and risk-based capital ratios would be
11.82%, 11.82% and 26.25%, respectively, at September 30, 1998.

LIQUIDITY

     The Bank is required to maintain minimum levels of liquid assets as defined
by OTS regulations. This requirement, which varies from time to time depending
upon


                                       12

<PAGE>


economic conditions and deposit flows, is based upon a percentage of deposits
and short-term borrowings. The required ratio currently is 5.0%. The Bank's
liquidity ratio averaged 20.49% during the month of September 30, 1998 and
24.17% during three months ended September 30, 1998. The Bank adjusts liquidity
as appropriate to meet its asset and liability management objectives.



YEAR 2000 CONSIDERATIONS

     The Company and the Bank rely on computers for the daily conduct of their
business and for data processing. There is concern among industry experts that
on January 1, 2000 computers will be unable to "read" the new year and there may
be widespread computer malfunctions. The Bank recognized that a comprehensive
and coordinated plan of action was needed to ensure readiness to perform Year
2000 processing. A Year 2000 Committee has been formed to implement the Year
2000 project, develop policies, document readiness of the Bank and the Company
to accommodate Year 2000 processing, and track and test progress towards full
compliance. The Bank contracts with a service bureau to provide the majority of
its data processing and is dependent upon purchased application software. In
house applications are limited to word-processing and spreadsheet functions.

RISK OF YEAR 2000 ISSUES

     To date, the Company has not identified any system which presents a
material risk of failing to be Year 2000 compliant in a timely manner, or for
which a suitable alternative cannot be implemented. However, as the Company
progresses with its Year 2000 transition, systems or equipment may be identified
which present a material risk of business interruption. Such disruption may
include the inability to process customer accounting transactions, including
deposits, withdrawals, loan payments and disbursements; the inability to
reconcile and record daily activity; the inability to process loan applications
or the track delinquencies; the inability to generate checks or to clear funds.
In addition, if any of the Company's major borrowers should fail to achieve Year
2000 compliance, and should they experience a disruption of their own
businesses, their ability to meet their obligations to the Company may be
serious impaired.

STATE OF READINESS

     The Bank is in the process of ensuring that its external vendors and its
data processing service provider are adequately addressing the system and
software issues related to the Year 2000 by obtaining written system
certifications that the systems are fully Year 2000 compliant or that the vendor
has a plan to become fully compliant by December 31, 1998. The Bank will utilize
the primary servicers, end-to-end tests, which will be available by December 31,
1998, to simulate daily processing on sensitive century dates. In the
evaluation, the Bank will ensure that critical operations will continue if
servicers or vendors are unable to achieve the Year 2000 requirements. The
Company does not anticipate that there will be any significant or material
condition which will impact the service provider's ability to deliver accurate
data processing services before, during and after the transition to the new
millennium, therefore no formal contingency plans exist at this time. However,
results of system tests conducted by the Company and by other users of this
service provider will be carefully monitored to ensure that all issues have been
identified and successfully remediated.

     The Committee has completed a systems inventory and obtained certification
from its service bureau. The Committee has identified critical applications and
implemented hardware system upgrades and system replacements. All upgrades have
been implemented and will be substantially tested for the Year 2000 compliance
by the first quarter of 1999. The Committee has budgeted $250,000 for hardware
system upgrades and system replacements, which has been approved by the Board of
Directors.

CONTINGENCY PLANS

     The Company is in the process of developing a contingency plan with its
primary servicer. The plan will identify components of applications which are
judged, at some point prior to December 31, 1999, to be at risk of failure to
achieve complete renovation, validation and implementation. The Contingency Plan
will ensure that the company has sufficiently planned for unanticipated system
failures at critical production dates before, on and after January 1, 2000.

     The discussion above contains certain forward-looking statements. Actual
results may differ materially from the Company's expectations due to the nature
and uncertainty of circumstances surrounding the Year 2000 problem. The Company
may fail to identify systems that are not Year 2000 compliant, or the Company or
other parties may fail to meet the dates and goals set above. If so, the extent
and nature of efforts to then address those contingencies, to repair or replace
the affected systems, the Company's ability to obtain qualified personnel,
consultants or other resources and the success of those efforts cannot be stated
with any degree to certainty.


                                       13


<PAGE>


ITEM 3.   QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

     There have been no material changes in information regarding quantitative
and qualitative disclosures about market risk as of September 30, 1998 from the
information as of March 31, 1998, which was disclosed in the Company's 1998 Form
10-K.





                                       14


<PAGE>


PART II. OTHER INFORMATION

Legal Proceedings

     In the normal course of business, the Company may be a party to various
outstanding legal proceedings and claims. In the opinion of management, the
financial position of the Company will not be materially affected by the outcome
of such legal proceedings and claims.

Changes in Securities
     Not applicable.

Defaults upon Senior Securities
     Not applicable.

Submission of Matters to Vote of Security Holders
     None.

Other Information

The Company announced on July 20, 1998 that it had entered into a definitive
agreement to merge with Richmond County Financial Corp., which agreement was
amended and restated on October 14, 1998. Under the terms of the agreement,
which is subject to approval by shareholders of each company and regulatory
authorities, the Company's shareholders will receive 1.05 shares of Richmond
County Financial Corp. common stock for each share of the Company owned. The
transaction is intended to be a tax-free merger accounted for as a purchase
transaction and is expected to be completed by the first quarter of calendar
1999. The Amended and Restated Agreement and Plan of Merger was included as an
exhibit to the Form 8-K filed by the Company on October 16, 1998.

Exhibits and Reports on Form 8-K

(a)  The following exhibits are filed as part of this report:

          3.1 Certificate of Incorporation of Bayonne Bancshares, Inc.*
          3.2  Bylaws of Bayonne Bancshares, Inc.*
          4.0  Stock Certificate of Bayonne Bancshares, Inc.*
         11.0  Computation of earnings per share (filed herewith)
         27.0  Financial Data Schedule (filed herewith)

(b)  A report on Form 8-K was filed on July 27, 1998 for the Agreement and Plan
     of Merger with Richmond County Financial Corp. The Company also filed a
     Form 8-K on October 16, 1998 to disclose the amendment and restatement of
     the Agreement and Plan of Merger


                                       15


<PAGE>
*Incorporated herein by reference in this document from the Exhibits to the Form
S-1 Registration Statement, filed on March 13, 1997, and any amendments thereto
(Registration No. 333-23199).




                                       16


<PAGE>



                                   SIGNATURES

     Pursuant to the requirements of Section 13 or 15(d) 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.


                              BAYONNE BANCSHARES, INC.


Date: November 13, 1998       By: /s/ MICHAEL A. NILAN
                                  ----------------------------------------------
                                      Michael A. Nilan
                                      President and Chief Executive Officer


Date: November 13, 1998       By: /s/ EUGENE V. MALINOWSKI
                                  ----------------------------------------------
                                      Eugene V. Malinowski
                                      Vice President and Chief Financial Officer




                                       17