SECURITIES AND EXCHANGE COMMISSION
                           WASHINGTON, D.C. 20549


                                  FORM 8-K


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

      DATE OF REPORT (DATE OF EARLIEST EVENT REPORTED): OCTOBER 7, 1998


                             GREATER BAY BANCORP
           (Exact name of registrant as specified in its charter)



          CALIFORNIA                                          77-0387041
(State or other jurisdiction of                            (I.R.S. employer
 incorporation or organization)                          identification number)


                      Commission file number:  0-25034
                                        

                           2860 WEST BAYSHORE ROAD
                         PALO ALTO, CALIFORNIA 94303
            (Address of principal executive offices and zip code)


     REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE: (650) 813-8200
                                        



                                        

 
ITEM 5.  OTHER EVENTS.

     Reference is hereby made to the Registrant's press releases attached
hereto as Exhibits 99.1 and 99.2 which meet the requirements for filing under
Item 5 and are incorporated herein by reference.

ITEM 7.  FINANCIAL STATEMENTS AND EXHIBITS.

Exhibits
- --------

99.1   Press Release dated October 7, 1998.

99.2   Press Release dated October 14, 1998.

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                                   SIGNATURES

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

                                      GREATER BAY BANCORP
                                      (Registrant)


 
Dated: October 16, 1998               By:  /s/ Steven C. Smith
                                           -------------------
                                           Steven C. Smith
                                           Executive Vice President, Chief
                                           Operating Officer and Chief Financial
                                           Officer

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                                EXHIBIT INDEX
                                -------------

99.1   Press Release dated October 7, 1998.

99.2   Press Release dated October 14, 1998.

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