EXHIBIT 99.2
                                        
                     Press Release dated November 27, 1998

For Immediate Release                   For Information Contact
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November 27, 1998                       David L. Kalkbrenner, President & CEO
                                        Greater Bay Bancorp (650) 614-5767
                                        Steven C. Smith, EVP, COO & CFO
                                        Greater Bay Bancorp (650) 813-8222


          GREATER BAY BANCORP ANNOUNCES CONSUMMATION OF ITS EXCHANGE 
                    OFFER FOR ITS FLOATING RATE SECURITIES,
                               SERIES A/SERIES B

PALO ALTO, CA., November 27, 1998 -- Greater Bay Bancorp (GBBK:Nasdaq) announced
today the consummation of its offer to exchange its $30 million aggregate
principal amount of Floating Rate Capital Securities, Series A, outstanding for
a like amount of its registered Floating Rate Capital Securities, Series B.  The
exchange offer was conducted in accordance with the terms of the initial
issuance of the Series A securities on August 12, 1998, and was made upon the
terms and conditions set forth in a Prospectus and in a related Letter of
Transmittal which were provided to holders of record of the Series A securities.
The expiration date of the exchange offer was November 23, 1998, and the
exchange offer was consummated on November 27, 1998.  All of the issued and
outstanding Series A securities were tendered and exchanged for a like amount of
Series B securities.

Greater Bay Bancorp and its financial services subsidiaries, Cupertino National
Bank, Mid-Peninsula Bank, Peninsula Bank of Commerce, Golden Gate Bank, along
with its operating divisions, Greater Bay Bank Santa Clara Valley Commercial
Banking Group, Greater Bay Corporate Finance Group, Greater Bay International
Banking Division, Greater Bay Trust Company, Pacific Business Funding and
Venture Banking Group, serve clients throughout Silicon Valley and the San
Francisco Peninsula with offices located in San Jose, Cupertino, Palo Alto,
Redwood City, San Mateo, Millbrae, San Bruno, San Francisco and Walnut Creek.

          This document may contain forward-looking statements that are subject
to risks and uncertainties that could cause actual results to differ materially
from those projected.  For a discussion of factors that could cause actual
results to differ, please see the Company's publicly available Securities and
Exchange Commission filings, including its Annual Report on Form 10-K for the
year ended December 31, 1997, and particularly the discussion of risk factors
within that document.

                         "WE INVEST IN RELATIONSHIPS"

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