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                     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): AUGUST 12, 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

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ITEM 5.  OTHER ITEMS.

     Greater Bay Bancorp (the "Registrant"), issued a press release on August
13, 1998 with respect to the completion of an offering of Cumulative Trust
Preferred Securities in an aggregate amount of $30 million through GBB Capital
II, a trust affiliate of the Registrant formed for the purpose of the offering.

ITEM 7.  FINANCIAL STATEMENTS AND EXHIBITS.

Financial Statements.
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Not Required.

Exhibits.
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4.1     Indenture between Greater Bay Bancorp and Wilmington Trust Company, as
        Debenture Trustee, dated as of August 12, 1998.

4.2     Floating Rate Junior Subordinated Deferrable Interest Debenture Due
        September 15, 2028 Series A /Series B, of Greater Bay Bancorp.

4.3     Registration Rights Agreement among Greater Bay Bancorp, GBB Capital II,
        and Sandler O'Neill & Partners, L.P., dated as of August 7, 1998.

4.4     Certificate of Trust of GBB Capital II, dated as of May 18, 1998.

4.5     Amended and Restated Trust Agreement of GBB Capital II, among Greater
        Bay Bancorp, Wilmington Trust Company and the Administrative Trustees
        named therein dated as of August 12, 1998.

4.6     Certificate Evidencing Common Securities of GBB Capital II.

4.7     Certificate Evidencing Capital Securities of GBB Capital II.

4.8     Common Securities Guarantee Agreement of Greater Bay Bancorp, dated as
        of August 12, 1998.

4.9     Series A Capital Securities Guarantee Agreement of Greater Bay Bancorp
        and Wilmington Trust Company, dated as of August 12, 1998.

4.10    Liquidated Damages Agreement among Greater Bay Bancorp, GBB Capital II,
        and Sandler O'Neill and Partners, L.P., dated as of August 7,
        1998.

99.1    Press Release dated August 13, 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)


 
                                       /s/ Steven C. Smith
Dated:  August 28, 1998             By___________________________________
                                         Steven C. Smith
                                         Executive Vice President, Chief
                                         Operating Officer and Chief Financial
                                         Officer

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                                EXHIBIT INDEX
                                -------------
Exhibits.
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4.1     Indenture between Greater Bay Bancorp and Wilmington Trust Company, as
        Debenture Trustee, dated as of August 12, 1998.

4.2     Floating Rate Junior Subordinated Deferrable Interest Debenture Due
        September 15, 2028 Series A /Series B, of Greater Bay Bancorp.

4.3     Registration Rights Agreement among Greater Bay Bancorp, GBB Capital II,
        and Sandler O'Neill & Partners, L.P., dated as of August 7, 1998.

4.4     Certificate of Trust of GBB Capital II, dated as of May 18, 1998.

4.5     Amended and Restated Trust Agreement of GBB Capital II, among Greater 
        Bay Bancorp, Wilmington Trust Company and the Administrative Trustees 
        named therein dated as of August 12, 1998.

4.6     Certificate Evidencing Common Securities of GBB Capital II.

4.7     Certificate Evidencing Capital Securities of GBB Capital II.

4.8     Common Securities Guarantee Agreement of Greater Bay Bancorp, dated as 
        of August 12, 1998.

4.9     Series A Capital Securities Guarantee Agreement of Greater Bay Bancorp
        and Wilmington Trust Company, dated as of August 12, 1998.

4.10    Liquidated Damages Agreement among Greater Bay Bancorp, GBB Capital II,
        and Sandler O'Neill and Partners, L.P., dated as of August 7,
        1998.

99.1    Press Release dated August 13, 1998.