Exhibit 4.1

                      APPOINTMENT OF SUCCESSOR RIGHTS AGENT


         This  instrument is dated as of December 13, 2004,  and entered into by
HRPT Properties  Trust, a Maryland real estate investment trust (the "Company"),
and Wells Fargo  Bank,  National  Association,  a national  banking  association
("Wells Fargo").

                                   BACKGROUND

         A. The parties hereto refer to the Renewed Rights  Agreement,  dated as
of March 10, 2004 (the "Rights  Agreement"),  between the Company and  EquiServe
Trust Company, N.A., a national banking association,  as Rights Agent thereunder
(in such capacity, the "Predecessor Rights Agent").

         B.  The  parties   further  refer  to  the  Terms  and   Conditions  of
Appointment,  adopted  by the  Company  on  August  12,  2004  (the  "Terms  and
Conditions"), providing, among things, for the appointment of Wells Fargo as the
transfer agent for the Company's  issued and  outstanding  capital shares and as
successor Rights Agent under the Right Agreement.

         C. This instrument is entered into in furtherance of the appointment of
Wells Fargo as successor Rights Agent under the Rights Agreement.

         NOW THEREFORE, the parties agree as follows:

         Section 1. The Company has heretofore  given notice to the  Predecessor
Rights  Agent of its  removal  as  Rights  Agent  under  the  Rights  Agreement,
effective  as of the date hereof  subject to the  appointment  of a successor in
accordance with Section 21 of the Rights Agreement.

         Section 2. Wells  Fargo  hereby  represents  to the  Company  that,  in
accordance  with  Section 21 of the  Rights  Agreement,  it is a legal  business
entity organized and doing business under the laws of the United States, in good
standing, authorized under such laws to exercise corporate trust, stock transfer
or shareholder services powers, subject to supervision or examination by federal
or  state  authority  and  has a  combined  capital  and  surplus  of  at  least
$100,000,000.

         Section 3. The Company hereby confirms that,  pursuant to the Terms and
Conditions,  it has appointed, and it does hereby appoint, Wells Fargo to act as
successor  to the  Predecessor  Rights  Agent as Rights  Agent  under the Rights
Agreement,  which  appointment  shall become effective at the Effective Time (as
defined below).

         Section 4. Wells Fargo hereby confirms that,  pursuant to the Terms and
Conditions,  it has accepted,  and it does hereby  accept,  its  appointment  as
successor  Rights Agent under the Right  Agreement  effective  at the  Effective
Time.

         Section 5. Pursuant and subject to Section 21 of the Rights  Agreement,
at the Effective Time Wells Fargo shall become and  thereafter  shall be a party
to the Rights  Agreement as Rights Agent thereunder and shall be vested with the
same powers,  rights,  duties and

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responsibilities  as if it had been  originally  named as Rights  Agent  without
further  act or deed of any  person or entity.  The  parties  acknowledge  their
intent that Wells Fargo does not assume and shall not have any responsibility or
liability for actions or omissions of the Predecessor  Rights Agent prior to the
Effective Time.

         Section 6. This instrument  shall become effective as of the opening of
business  in New York  City on the date  first  above  written  (the  "Effective
Time").

         Section 7. For  purposes  of Section  25 of the Rights  Agreement,  the
address of Wells Fargo as Rights  Agent  thereunder  for  purposes of notices or
demands  (until  another  address is filed in  writing by Wells  Fargo as Rights
Agent with the Company)  shall be as set forth under Wells Fargo's  signature to
this instrument.

         Section 8. All the  covenants and  provisions of this  instrument by or
for the benefit of the  Company or the Rights  Agent shall bind and inure to the
benefit of their respective successors and assigns under the Rights Agreement.

         Section 9. This instrument  shall be deemed to be a contract made under
the laws of the State of Maryland  and shall for all purposes be governed by and
construed in  accordance  with the laws of the State of Maryland  applicable  to
contracts  made and to be  performed  entirely  within  the  State of  Maryland,
including its principles of conflicts of law.

         Section  10.  This   instrument  may  be  executed  in  any  number  of
counterparts and each of such  counterparts  shall for all purposes be deemed to
be an original,  and all such counterparts shall together constitute but one and
the same instrument.

         IN WITNESS  WHEREOF,  the parties hereto have caused this instrument to
be duly executed under seal as of the day and year first above written.

[SEAL]                                       WELLS FARGO BANK, NATIONAL
                                             ASSOCIATION



ATTEST:                                      By: /s/ Claudine Anderson
                                                 Name:  Claudine Anderson
                                                 Title: Officer
By: /s/ Susan J. Roeder
    Name:  Susan J. Roeder
    Title: Assistant Secretary
                                             Address:

                                             Wells Fargo Shareowner Services
                                             161 N. Concord Exchange
                                             South St. Paul, MN 55075
                                             Attention:  Claudine Anderson

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[SEAL]                                       HRPT PROPERTIES TRUST



ATTEST:                                      By: /s/ John A. Mannix
                                                 Name:  John A. Mannix
                                                 Title: President and Chief
                                                 Operating Officer
By: /s/ Jennifer B. Clark
    Name:  Jennifer B. Clark
    Title: Assistant Secretary















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