SECURITIES AND EXCHANGE COMMISSION WASHINGTON, D.C.

                                      FORM 8-K
  
                                   CURRENT FORM
                       PURSUANT TO SECTION 13 OR 15(d) OF THE
                           SECURITIES EXCHANGE ACT OF 1934


Date of report (Date of earliest event reported) :  March 31, 1998

                                  NSS Bancorp, Inc.               
                 (Exact Name of Registrant as Specified in Charter)

Connecticut                      0-22937                  06-1485317   
(State or Other Jurisdiction     (Commission              (IRS Employer
of Incorporation)                 File Number)             Identification
                                                           No.)

48 Wall Street,              Norwalk, Connecticut         06852       
(Address of Principal Executive Offices)                  (Zip Code)


Registrant's telephone number, include area code:     203-838-4545



                                        N/A               
          (Former Name or Former Address, if Changed Since Last Report)



Item 5.  Other Events.

      A copy of the Company's press release announcing an extension of its 
stock repurchase program until December 31, 1998 is attached hereto as 
Schedule A.


                                SIGNATURES

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

April 2, 1998                           NSS Bancorp, Inc.
                                            Registrant


                                            By: /s/ Robert T. Judson
                                                Robert T. Judson
                                                President                     

Schedule A

                                NSS BANCORP, INC.
                                 48 Wall Street
                               Norwalk, CT  06852


FOR IMMEDIATE RELEASE                             Contact: Marc I. Braverman
Tuesday, March 31, 1998                                    Senior V.P. & CFO
                                                                203-899-2515




NSS BANCORP, INC. ANNOUNCES EXTENSION
TO ITS STOCK REPURCHASE PROGRAM


      NSS Bancorp,Inc. (NASDAQ: NSSY) announced today that its Board of
Directors has extended the stock repurchase program orginally announced on
December 1, 1997.  The program authorizes the Company to repurchase up to
15% of its issued and outstanding common stock at market prices in
negotiated and/or open market purchases.  The Company is not obligated to
make any purchases but may do so at any time until December 31, 1998,
unless extended by the Board of Directors.