EXHIBIT 99.1


                     Press Release dated November 18, 1998



FOR IMMEDIATE RELEASE                   FOR INFORMATION CONTACT

                                        David L. Kalkbrenner, President & CEO
                                        (650) 614-5767
                                        Steven C. Smith, EVP, COO & CFO
                                        (650) 813-8222
 

                              GREATER BAY BANCORP
                        ADOPTS SHAREHOLDER RIGHTS PLAN

  PALO ALTO, CA: November 18, 1998 -- Greater Bay Bancorp (Nasdaq:GBBK)
announced that its Board of Directors has adopted a shareholder rights plan
designed to maximize the long-term value of the Company and to protect the
Company's shareholders from improper takeover tactics and takeover bids that are
not fair to all shareholders.

  According to David L. Kalkbrenner, the Company's President and Chief Executive
Officer, "The rights are not designed to prevent an appropriate acquisition of
the Company.  Rather, the rights plan should encourage anyone interested in
acquiring the Company to negotiate with the Board of Directors prior to
attempting an acquisition.  We believe this will assure that all of our
shareholders receive fair and equal treatment and are able to receive the long-
term value of their investment in the Company."

  In accordance with the plan, preferred share purchase rights will be
distributed as a dividend at the rate of one right for each common share held of
record as of the close of business on November 30, 1998.  The rights, which are
not immediately exercisable, entitle the holders to purchase one one-hundredth
of a share of Series A Preferred Stock at a price of $145.00 upon the occurrence
of certain triggering events.  In the event of an acquisition not approved by
the Board, each right enables its holder (other than the acquirer) to purchase
the Preferred Stock at 50% of the market price.  Further, in the event the
Company is acquired in an unwanted merger or business combination, each right
enables the holder to purchase shares of the acquiring entity at a similar
discount.  Under certain circumstances, the rights may be exchanged for common
shares of the Company.  The Board may, in its sole discretion, redeem the rights
at any time prior to any of the triggering events.

  The rights can be exercised and separate rights certificates distributed only
if any of the following events occur:  acquisition by a person of 10% or more of
the Company's common shares; a tender offer for 10% or more of the Company's
common shares; or ownership of 10% or more of the Company's common shares by a
shareholder whose actions are likely to have a 

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material adverse impact on the Company or shareholder interests. The rights will
initially trade automatically with the common shares. The rights are not deemed
by the Board of Directors to be presently exercisable.

  Greater Bay Bancorp and its financial services subsidiaries, Cupertino
National Bank, Mid-Peninsula Bank, Peninsula Bank of Commerce and 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 Group, 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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