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Exhibit 10.7.18

AGREEMENT

        This Agreement, dated as of September 17, 2003 ("Agreement"), between
Arch Capital Group Ltd., a Bermuda corporation (the "Company"), and John D.
Vollaro (the "Executive") amends certain terms of the Employment Agreement (as
defined herein) and the Restricted Share Agreements (as defined herein) as
follows.

        The parties hereto agree as follows.

1.Reference is hereby made to the Restricted Share Agreement, dated as of
February 20, 2003 (the "February Restricted Share Agreement"), between the
Company and the Executive, the Restricted Share Agreement, dated as of
January 18, 2002 (the "January Restricted Share Agreement" and, together with
the February Restricted Share Agreement, the "Restricted Share Agreements"),
between the Company and the Executive, as amended by Amendment No. 1, made as of
March 19, 2003.

a.the first sentence of Section 2(a) of the January Restricted Share Agreement
shall be amended and restated as follows:

"(a) Vesting of Award. Subject to Section 2(b) below and the other terms and
conditions of this Agreement, this Award shall become vested on December 30,
2004."

b.the first sentence of Section 2(a) of the February Restricted Share Agreement
shall be amended and restated as follows:  

"(a) Vesting of Award. Subject to Section 2(b) below and the other terms and
conditions of this Agreement, this Award, to the extent not already vested,
shall become vested in two installments as follows: (i) 1,838 Restricted Shares
of the Award on February 20, 2004 and (ii) 3,674 Restricted Shares of the Award
on December 30, 2004."

2.Reference is hereby made to the Employment Agreement ("Employment Agreement"),
dated as of January 18, 2002, between the Company and the Executive.

a.The second sentence of Section 9.01 of the Employment Agreement is amended and
restated as follows:

"In addition, the Executive hereby agrees that at any time during the Employment
Period, and for a period ending two (2) years after the termination of the
Executive's employment if such termination is for Cause or as a result of the
Executive's resignation or leaving employment not for Good Reason (the
"Noncompetition Period"), he will not directly or indirectly own, manage,
control, participate in, consult with, render services for or in any manner
engage in any business competing with the businesses of the Company or its
Subsidiaries as such businesses exist or are in process or being planned as of
the date of termination, within any geographical area in which the Company or
its Subsidiaries engage or plan to engage in such businesses; provided, that, in
no event shall the Noncompetition Period end earlier than January 18, 2007 in
cases where the termination of Executive's employment is for Cause or as a
result of the Executive's resignation or leaving employment not for Good
Reason."

3.All other provisions of each of the Restricted Share Agreements and the
Employment Agreement shall remain in full force and effect. This Agreement may
be executed in two counterparts, each of which shall constitute one and the same
instrument.

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        IN WITNESS WHEREOF, the parties hereto have executed this Agreement as
of the date and year first above written.

    ARCH CAPITAL GROUP LTD.
 
 
By:
/s/  CONSTANTINE IORDANOU      

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Printed Name:  Constantine Iordanou
Title:  President and Chief Executive Officer
 
 
/s/  JOHN D. VOLLARO      

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John D. Vollaro

2

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Exhibit 10.7.18

AGREEMENT