SCHEDULE 14A INFORMATION

                 Proxy Statement Pursuant to Section 14(a) of
           the Securities Exchange Act of 1934 (Amendment No.     )


Filed by the Registrant [X]
Filed by a Party other than the Registrant [_]
Check the appropriate box:
[_]  Preliminary Proxy Statement
[_]  Confidential, for Use of the Commission Only (as permitted by Rule 14a-
     6(e)(2))
[_]  Definitive Proxy Statement
[X]  Definitive Additional Materials
[_]  Soliciting Material Pursuant to Rule 14a-11(c) or Rule 14a-12

                              GREATER BAY BANCORP
               (Name of Registrant as Specified In Its Charter)

 ....................................N/A.........................................
(Name of Person(s) Filing Proxy Statement, if other than the Registrant)

Payment of Filing Fee (Check the appropriate box):

[X] No fee required
[_] $125 per Exchange Act Rules 0-11(c)(1)(ii), 14a-6(i)(1), 14a-6b(i)(2) or
    Item 22(a)(2) of Schedule 14A.
[_] Fee computed on table below per Exchange Act Rules 14a-6(i)(4) and 0-11.

(1)  Title of each class of securities to which transaction applies:
     ...........................................................................
(2)  Aggregate number of securities to which transaction applies:
     ...........................................................................
(3)  Per unit price or other underlying value of transaction computed pursuant
     to Exchange Act Rule 0-11 (set forth the amount on which the filing fee is
     calculated and state how it was determined):
     ...........................................................................
(4)  Proposed maximum aggregate value of transaction:
     ...........................................................................
(5)  Total fee paid:
     ...........................................................................
[_]  Fee paid previously with preliminary materials.
[_]  Check box if any part of the fee is offset as provided by Exchange Act Rule
0-11(a)(2) and identify the filing for which the offsetting fee was paid
previously. Identify the previous filing by registration statement number, or
the Form or Schedule and the date of its filing.

(1)  Amount Previously Paid: ___________
 
(2)  Form, Schedule or Registration Statement No.: ______________
 
(3)  Filing Party: ______________________________________________
 
(4)  Date Filed: _______________________



 
April 9. 1999



A Message to Our Shareholders,

If you were a holder of Bay Area Bancshares common stock as of the close of 
business on Friday, March 19, 1999, you should have received a Notice of 
Special Meeting and a Proxy Statement/Prospectus relating to the approval of 
the merger of Bay Area Bancshares with Greater Bay Bancorp. Your vote is very 
important. We cannot complete the merger unless the shareholders of Bay Area 
Bancshares approve the merger agreement.

If you have not yet voted your shares, we encourage you to do so on the Proxy
Card which was enclosed with the Proxy Statement/Prospectus. If you did not
receive this information and you hold your stock in certificate form, please
call Janeene Johnson at our toll free number: 1-888-257-1600 to have a proxy
card sent to you. If your stock is held in a brokerage account, you should
telephone your broker and request that the proxy information be forwarded to
you immediately.

We appreciate your prompt attention to this very important matter.

THE BOARD OF DIRECTORS OF BAY AREA BANCSHARES