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                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C.  20549



                                    FORM 8-K

                                 CURRENT REPORT
   Pursuant to Section 13 or 15(d) of the Securities and Exchange Act of 1934

        Date of Report (date of Earliest Event Reported):  May 12, 1997


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

        CALIFORNIA                       0-25034               77-0387041
(State or other jurisdiction    (Commission File Number)  (I.R.S. Employer
 of incorporation or                                      Identification Number)
 organization)                                        
           

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


      REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE:   (415) 813-8200

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ITEM 1.   CHANGES IN CONTROL OF REGISTRANT.

          Not applicable.

ITEM 2.   ACQUISITION OR DISPOSITION OF ASSETS.

          Not applicable.

ITEM 3.   BANKRUPTCY OR RECEIVERSHIP.

          Not applicable.

ITEM 4.   CHANGES IN REGISTRANT'S CERTIFYING ACCOUNTANT.

          Not applicable.

ITEM 5.   OTHER EVENTS.

          A.   Amendments of Articles of Incorporation and Bylaws.

          Effective May 12, 1997, a majority of the outstanding shares of common
stock, no par value ("Common Stock"), of Greater Bay Bancorp (the "Company")
approved by written consent proposals (the "Proposals") to (i) amend the
Company's Articles of Incorporation to eliminate cumulative voting in the
election of directors, and (ii) amend the Company's Bylaws to provide for the
classification of the Company's Board of Directors for purposes of the election
of directors.

          B.   Consummation of Trust Preferred Securities Offering.

          On March 31, 1997, the Company, through its wholly-owned subsidiary,
GBB Capital I, a Delaware statutory business trust, consummated a $20 million
offering (the "Offering") of GBB Capital I's 9.75% cumulative trust preferred
securities.  GBB Capital I invested the proceeds of the Offering in 9.75% Junior
Subordinated Deferrable Interest Debentures (the "Debentures") issued by the
Company.

ITEM 6.   RESIGNATIONS OF REGISTRANT'S DIRECTORS.

          Not applicable.

ITEM 7.   FINANCIAL STATEMENTS AND EXHIBITS.

     (a)  Financial Statements.

          Not applicable.

     (b) Pro Forma Financial Statements.

          Not applicable.

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     (c)  Exhibits.

          3.1  Articles of Incorporation of Greater Bay Bancorp, as amended.

          3.2  Bylaws of Greater Bay Bancorp, as amended.

          4.1  Junior Subordinated Indenture between Greater Bay Bancorp and
Wilmington Trust Company, as Trustee, dated as of March 31, 1997.

          4.2  Officer's Certificate and Company Order, dated March 31, 1997.

          4.3  Reserved.

          4.4  Reserved.

          4.5  Reserved.

          4.6  Amended and Restated Trust Agreement of GBB Capital I among
Greater Bay Bancorp, as Depositor, Wilmington Trust Company, as Property Trustee
and Delaware Trustee, and the Administrative Trustees named therein, dated as of
March 31, 1997.
 
          4.7  Trust Preferred Certificate of GBB Capital I.

          4.8  Common Securities Certificate of GBB Capital I.

          4.9  Guarantee Agreement between Greater Bay Bancorp, as Guarantor,
and Wilmington Trust Company, as Trustee, dated as of March 31, 1997.

          4.10 Agreement as to Expenses and Liabilities, dated as of March 31,
1997.

          4.11 Reserved.

          4.12 Reserved.

          4.13 Reserved.

          4.14 Supplemental Debenture Agreement, dated as of March 27, 1997.

ITEM 8.   CHANGE IN FISCAL YEAR.

          Not applicable.

ITEM 9.   SALES OF EQUITY SECURITIES PURSUANT TO REGULATION S.

          Not applicable.

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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 hereunto duly authorized.

                                         GREATER BAY BANCORP



Dated:  June 2, 1997                     /s/ Steven C. Smith
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                                         Steven C. Smith
                                         Executive Vice President,
                                         Chief Operating Officer and
                                         Chief Financial Officer

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