EXHIBIT 99



FOR IMMEDIATE RELEASE                   FOR INFORMATION CONTACT
- ---------------------                   -----------------------

                                        DAVID L. KALKBRENNER, PRESIDENT & CEO
                                          GREATER BAY BANCORP (650) 614-5767
                                        STEVEN C. SMITH, EVP, COO & CFO
OCTOBER 23, 1998                          GREATER BAY BANCORP (650) 813-8222



                   GREATER BAY BANCORP ANNOUNCES EXCHANGE
                OFFER FOR FLOATING RATE SECURITIES, SERIES A

        PALO ALTO, CA; October 23, 1998. -- Greater Bay Bancorp (Nasdaq:GBBK) 
announced today the commencement of an 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 is being conducted in accordance with 
the terms of the initial issuance of the Series A securities on August 12, 
1998, and is being made upon the terms and conditions set forth in a Prospectus
and in a related Letter of Transmittal which are being provided to holders of 
record of the Series A securities.

        The exchange offer is not conditioned on any amount of the Series A 
securities being exchanged. The exchange offer is scheduled to expire at 5:00 
p.m., Eastern Time, on November 23, 1998, unless extended.

        This documents 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 Greater Bay Bancorp's 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"