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                                                                    Exhibit 4.35

                       LIQUIDATED DAMAGES AGREEMENT


     THIS LIQUIDATED DAMAGES AGREEMENT (the "Agreement") is made and entered
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into as of May 16, 2000 by and among GREATER BAY BANCORP, a California
corporation (the "Company"), GBB CAPITAL IV, a business trust formed under the
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laws of the state of Delaware (the "Trust") and SANDLER O'NEILL & PARTNERS,
                                    -----
L.P., as representative of the initial purchasers named in Schedule A of the
Purchase Agreement (the "Initial Purchasers").
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     WHEREAS, as an inducement to the Initial Purchasers to enter into the
Purchase Agreement, dated May 16, 2000 (the "Purchase Agreement"), by and among
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the Company, the Trust and the Initial Purchasers (providing for, among other
things, the sale by the Trust to the Initial Purchasers of 41,000 of the Trust's
10.75% Capital Securities, Series A, liquidation amount of $1,000 per Capital
Security (the "Capital Securities"), the proceeds of which will be used by the
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Trust to purchase 10.75% Junior Subordinated Deferrable Interest Debentures due
June 1, 2030, Series A, of the Company (the "Subordinated Debentures")), and as
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a condition to the several obligations of the Initial Purchasers thereunder, the
Company and the Trust have agreed to provide to the Initial Purchasers and their
direct and indirect transferees certain registration and related rights pursuant
to and in accordance with the terms of the Registration Rights Agreement, dated
the date hereof (the "Registration Rights Agreement"), by and among the Company,
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the Trust and the Initial Purchasers; and

     WHEREAS, notwithstanding the fact that the Company and the Trust have
consummated or will consummate an Exchange Offer, pursuant to Section 2(b) of
the Registration Rights Agreement, the Initial Purchasers may, under certain
circumstances, require the Company and the Trust to file a Shelf Registration
Statement for the resale of certain Registrable Securities held by it;

     WHEREAS, the Registration Rights Agreement contains certain provisions
concerning the time within which the Company and the Trust must file the Shelf
Registration Statement and the period for which such Shelf Registration
Statement must remain effective and usable for resales; and

     WHEREAS, the Company, the Trust and the Initial Purchasers desire to
provide for the payment of liquidated damages by the Company directly to the
Initial Purchasers in the event that the Company and the Trust fail to comply
with such contractual provisions, as more fully set forth herein.

     NOW, THEREFORE, in consideration of the foregoing, and for other good and
valuable consideration the receipt of which is hereby acknowledged, the parties
hereto agree as follows:

     1.   Definitions. Capitalized terms used (including in the foregoing
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recitals) but not defined herein shall have the meanings given to such terms in
the Registration Rights Agreement, except that (a) the term "Shelf Registration
Statement" shall refer only to a Shelf Registration Statement filed by the
Company and the Trust pursuant to Section 2(b) of the Registration Rights
Agreement, and (b) the term "Registrable Securities" shall refer only to those
Registrable Securities held at such time by the Initial Purchasers.

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     2.   Payment of Liquidated Damages. (a) In the event that (i) the Shelf
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Registration Statement is not filed with the SEC on or prior to the 45/th/ day
after a request for such filing is properly made by the Initial Purchasers in
accordance with Section 2(b) of the Registration Rights Agreement (provided that
in no event shall such date be required to be earlier than 75 days after the
Issue Date), or (ii) the Shelf Registration Statement is not declared effective
by the SEC on or prior to the later of the 40th day after the date such Shelf
Registration Statement was required to be filed pursuant to the terms of the
Registration Rights Agreement and the 180th date after the Issue Date, or (iii)
the Shelf Registration Statement has been declared effective and such Shelf
Registration Statement ceases to be continuously effective or usable for resales
(whether as a result of an event contemplated by Section 3(e) of the
Registration Rights Agreement or otherwise) at any time during the 180-day
period (and any extensions of such period pursuant to the last paragraph of
Section 3 of the Registration Rights Agreement) immediately following the date
on which the Shelf Registration Statement is first declared effective (other
than after such time as all Registrable Securities have been disposed of
thereunder or otherwise cease to be Registrable Securities pursuant to the terms
of the Registration Rights Agreement), then in each case the Company shall pay
liquidated damages to the Initial Purchasers, at a rate of 25 basis points per
annum in respect of the aggregate liquidation amount of Capital Securities held
by the Initial Purchasers or, in the event that the Trust is liquidated and
Subordinated Debentures are distributed to holders of Capital Securities, the
aggregate principal amount of Subordinated Debentures held by the Initial
Purchasers, as the case may be, in respect of the period (x) commencing on the
46th day after such request for the filing of a Shelf Registration Statement is
made by the Initial Purchasers (provided that in no event shall such date be
required to be earlier than 76 days after the Issue Date) and terminating upon
the filing of the Shelf Registration Statement (in the case of clause (i)
above), (y) commencing on the later of the 41st day after the date the Shelf
Registration Statement was required to be filed and the 181st day after the
Issue Date and terminating upon the effectiveness of the Shelf Registration
Statement (in the case of clause (ii) above), or (z) commencing on the day the
Shelf Registration Statement ceases to be effective or usable for resales and
terminating at such time as the Shelf Registration Statement again becomes
effective and usable for resales (in the case of clause (iii) above), provided,
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however, that the maximum aggregate amount of liquidated damages payable by the
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Company pursuant to this Agreement and the Registration Rights Agreement shall
not exceed 25 basis points per annum in respect of the aggregate liquidation
amount of the Capital Securities or, in the event the Trust is liquidated and
Subordinated Debentures are distributed to holders of Capital Securities, the
aggregate principal amount of Subordinated Debentures.

     (b)  Any amounts of liquidated damages payable by the Company pursuant to
this Section 2 shall be paid in cash directly to the Initial Purchasers on the
next succeeding June 1st, and December 1st, as the case may be, following the
period in respect of which such Liquidated Damages have become due and payable
hereunder.

     3.   General.
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     (a)  Counterparts. This Agreement may be executed in any number of
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          counterparts and by the parties hereto in separate counterparts, each
          of which when so

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          executed shall be deemed to be an original and all of which taken
          together shall constitute one and the same agreement.

     (b)  Amendments. This Agreement may be amended by the parties hereto by a
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          written instrument duly executed on behalf of each of the parties
          hereto.

     (c)  Entire Agreement. This Agreement and the Registration Rights Agreement
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          constitute the entire agreement, and supersede all prior agreements
          and understandings, both written and oral, among the parties with
          respect to the subject matter hereof.

     (d)  Governing Law. This Agreement shall be governed by and construed in
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          accordance with the laws of the State of New York, without regard to
          any applicable conflicts of law principles.

     (e)  Notices.  All notices and other communications hereunder shall be in
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          writing and shall be deemed given if delivered to the parties at the
          addresses set forth in, and in a manner contemplated by, the
          Registration Rights Agreement.

     (f)  Effective Date.  This Agreement shall be of no force and effect and
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          the parties shall have no obligations or rights hereunder until the
          Closing Time whereupon this Agreement shall be effective.

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          IN WITNESS WHEREOF, the parties have executed this Liquidated Damages
Agreement as of the date first written above.

                              GREATER BAY BANCORP

                              By:  /s/ Steven C. Smith
                                   _____________________________________________
                                   Name:
                                   Title:


                              GBB CAPITAL IV


                              By:  Greater Bay Bancorp,
                                   as Sponsor


                              By:/s/ Steven C. Smith
                                 _______________________________________________

                                   Name:
                                   Title:


                              SANDLER O'NEILL & PARTNERS, L.P.


                              Acting severally on behalf of itself and
                              representative of the Several Initial Purchasers
                              named in Schedule A of the Purchase Agreement


                              By:  SANDLER O'NEILL & PARTNERS CORP.,
                                   the sole general partner


                              By:  /s/ Catherine A. Lawton
                                   _____________________________________________
                                   Catherine A. Lawton
                                   Vice President

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