<PAGE>

                                                                    Exhibit 3.34

                    AMENDMENT NO. 29 TO AMENDED AND RESTATED
                        AGREEMENT OF LIMITED PARTNERSHIP
                           OF PRIME GROUP REALTY, L.P.

         This AMENDMENT NO. 29 TO AMENDED AND RESTATED AGREEMENT OF LIMITED
PARTNERSHIP OF PRIME GROUP REALTY, L.P. (this "Amendment") is made as of October
15, 1999 by Prime Group Realty Trust, a Maryland real estate investment trust
("PGRT"), as the Managing General Partner of Prime Group Realty, L.P., a
Delaware limited partnership (the "Partnership"), and on behalf of the other
Partners (as hereinafter defined). Capitalized terms used but not otherwise
defined herein shall have the meanings given to such terms in the Amended and
Restated Agreement of Limited Partnership of the Partnership, dated as of
November 17, 1997, by and among PGRT and the other parties signatory thereto, as
amended thereafter (as so amended, the "Limited Partnership Agreement").

                              W I T N E S S E T H:

         WHEREAS, pursuant to Section 4.3.C. of the Limited Partnership
Agreement, the Managing General Partner may raise all or any portion of
Additional Funds required by the Partnership for the acquisition of additional
properties by accepting additional Capital Contributions, including the issuance
of Common Units for Capital Contributions that consist of property or interests
in property;

         WHEREAS, pursuant to that certain Exchange Agreement dated as of
December 15, 1997 by and between H Group LLC, a Delaware limited liability
company ("HG"), and the Partnership (the "Exchange Agreement"), HG agreed, among
other things, to grant to the Partnership an option (the "First Option") to
exchange the Underlying Option (as defined in the Exchange Agreement) for
220,000 Common Units of Limited Partner Interest (subject to adjustment pursuant
to the terms of the Exchange Agreement), which grant of the First Option
contemplated the transfer by the Partnership to HG of 5,000 Common Units of
Limited Partner Interest on the date thereof and, subject to the terms of the
First Option, 5,000 Common Units of Limited Partner Interest (subject to
adjustment pursuant to the terms of the Exchange Agreement) on the 15th day of
each month thereafter (each such transfer a "First Option Maintenance Transfer")
for such number of months set forth in the Exchange Agreement;

         WHEREAS, the Partnership has agreed to the terms of the grant by HG of
the First Option set forth in the Exchange Agreement and desires to effect the
First Option Maintenance Transfer due on October 15, 1999;

         WHEREAS, HG was admitted to the Partnership as an Additional Limited
Partner as of December 15, 1997 pursuant to Amendment No. 2 to the Limited
Partnership Agreement;

         WHEREAS, the Partners desire to amend the Limited Partnership Agreement
to reflect the increase in outstanding Common Units resulting from the issuance
of Common Units to HG in connection with the First Option Maintenance Transfer
due on October 15, 1999; and


<PAGE>


         WHEREAS, Sections 2.4 and 12.3 of the Limited Partnership Agreement
authorize, among other things, the Managing General Partner, as true and lawful
agent and attorney-in fact, to execute, swear to, acknowledge, deliver, file and
record this Amendment on behalf of each Partner that has executed the Limited
Partnership Agreement and on behalf of the Partnership.

         NOW, THEREFORE, for good and adequate consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties hereto agree as
follows:

         Section 1. ACCEPTANCE OF CAPITAL CONTRIBUTION IN EXCHANGE FOR COMMON
UNITS. (a) PGRT, as Managing General Partner and on behalf of the Partnership,
hereby accepts the grant of the rights consisting of the First Option during the
twenty-third month of the term of the First Option from HG as a Capital
Contribution having a value on the date hereof of $100,000, in exchange for
6494.0 Common Units of Limited Partner Interest which are hereby issued by the
Partnership to HG pursuant to Section 4.3.C. of the Limited Partnership
Agreement, and which are evidenced by Common Unit Certificate No. 52 of the
Partnership.

                  (b) Each of the Common Units of Limited Partner Interest
issued to HG pursuant to this SECTION 1 shall have the same terms and provisions
of the Common Units of Limited Partner Interest issued by the Partnership on
November 17, 1997 except that (i) the Exchange Rights relating thereto may be
exercised at any time after December 15, 1999 (as opposed to November 17, 1998)
and (ii) such Common Units of Limited Partner Interest will be subject to the
Registration Rights Agreement dated as of December 15, 1997 by and among PGRT,
the Partnership and HG as opposed to the Registration Rights Agreement entered
into by PGRT and the Partnership on November 17, 1997.

         Section 2. AMENDMENT OF EXHIBIT A TO THE LIMITED PARTNERSHIP AGREEMENT.
Exhibit A to the Limited Partnership Agreement is hereby amended and restated to
reflect the aforementioned change(s) by deleting Exhibit A attached thereto in
its entirety, and by attaching in lieu thereof a replacement exhibit in the form
of EXHIBIT A attached hereto. From and after the effectiveness of this
Amendment, the amended and restated EXHIBIT A attached hereto shall be the only
Exhibit A to the Limited Partnership Agreement, unless and until it is hereafter
further amended.

         Section 3. REFERENCE TO AND EFFECT ON THE LIMITED PARTNERSHIP
AGREEMENT.

                  A. The Limited Partnership Agreement is hereby deemed to be
amended to the extent necessary to effect the matters contemplated by this
Amendment. Except as specifically provided for hereinabove, the provisions of
the Limited Partnership Agreement shall remain in full force and effect.

                  B. The execution, delivery and effectiveness of this Amendment
shall not operate (i) as a waiver of any provision, right or obligation of the
Managing General Partner, the other General Partner or any Limited Partner under
the Limited Partnership Agreement except as specifically set forth herein or
(ii) as a waiver or consent to any subsequent action or transaction.

         Section 4. APPLICABLE LAW. This Amendment shall be construed in
accordance with and governed by the laws of the State of Delaware, without
regard to the principles of conflicts of law.


                                      -2-
<PAGE>


                                       AMENDMENT NO. 29 TO AMENDED AND
                                       RESTATED AGREEMENT OF LIMITED
                                       PARTNERSHIP OF PRIME GROUP REALTY, L.P.

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

                                MANAGING GENERAL PARTNER:

                                PRIME GROUP REALTY TRUST, a
                                Maryland real estate investment trust

                                By:__________________________

                                Name:

                                Title:

                                LIMITED PARTNERS:

                                Each Limited Partner hereby executes
                                this Amendment to the Limited
                                Partnership Agreement.

                                By:      PRIME GROUP REALTY TRUST, a
                                         Maryland real estate investment
                                         trust, as attorney-in fact

                                         By:__________________________

                                         Name:

                                         Title:


                                      -3-
<PAGE>


                                   EXHIBIT A*

               PARTNERS, NUMBER OF UNITS AND CAPITAL CONTRIBUTIONS
<TABLE>
<CAPTION>
                                                 Number of               Capital
Managing General Partner                       Common Units            Contribution
------------------------                       ------------            ------------
<S>                                            <C>                      <C>
Prime Group Realty Trust                       15,135,827               **
         77 West Wacker Drive
         Suite 3900
         Chicago, IL 60601
         Attn:  Richard S. Curto
                James F. Hoffman

General Partner
---------------
                                                  927,100               $18,542,000
The Nardi Group, L.L.C
         c/o Stephen J. Nardi
         4100 Madison Street
         Hillside, IL 60162

Limited Partners
----------------
The Nardi Group, L.L.C                            328,182                $4,906,061
         c/o Stephen J. Nardi
         4100 Madison Street
         Hillside, IL 60162

Edward S. Hadesman                                388,677                $7,773,540
Trust Dated May 22, 1992
         c/o Edward S. Hadesman
         2500 North Lakeview
       Unit 1401
         Chicago, IL 60614
Grandville/Northwestern                             9,750                  $195,000
Management Corporation
         c/o Edward S. Hadesman
         2500 North Lakeview
       Unit 1401
         Chicago, IL 60614
</TABLE>
------------------

* As amended by Amendment No. 29 to the Amended and Restated Agreement of
  Limited Partnership of Prime Group Realty, L.P.

** This amount shall be inserted by the Managing General Partner.


<PAGE>


<TABLE>
<CAPTION>
                                                 Number of       Capital
Managing General Partner                       Common Units    Contribution
------------------------                       ------------    ------------
<S>                                            <C>              <C>

Carolyn B. Hadesman                                54,544       $1,090,880
Trust Dated May 21, 1992
         c/o Edward S. Hadesman
         2500 North Lakeview
       Unit 1401
         Chicago, IL 60614

Lisa Hadesman 1991 Trust                          169,053       $3,381,060
         c/o Edward S. Hadesman
         2500 North Lakeview
Unit 1401
         Chicago, IL 60614

Cynthia Hadesman 1991 Trust                       169,053       $3,381,060
         c/o Edward S. Hadesman
         2500 North Lakeview
       Unit 1401
         Chicago, IL 60614

Tucker B. Magid                                    33,085         $661,700
         545 Ridge Road
         Highland Park, IL 60035

Frances S. Shubert                                 28,805         $576,100
         511 Lynn Terrace
         Waukegan, IL 60085

Grandville Road Property, Inc.                      7,201         $144,020
         c/o Ms. Frances S
     Shubert
         511 Lynn Terrace
         Waukegan, IL 60085

Sky Harbor Associates                              62,149       $1,242,980
         c/o Howard I. Bernstein
         6541 North Kilbourn
         Lincolnwood, IL 60646

Jeffrey A. Patterson                              110,000       $2,200,000
         c/o Prime Group Realty Trust
         77 West Wacker Drive
         Suite 3900
         Chicago, IL 60601

Primestone Investment Partners, L.P.            7,944,893             **
         c/o The Prime Group, Inc.
         77 West Wacker Drive
         Suite 3900
         Chicago, IL 60601
         Attn:  Paul A. Roehri
</TABLE>
----------------------------

** This amount shall be inserted by the Managing General Partner.


                                   EXHIBIT A-2
<PAGE>


<TABLE>
<CAPTION>
                                                 Number of       Capital
Managing General Partner                       Common Units    Contribution
------------------------                       ------------    ------------
<S>                                            <C>              <C>

Prime Group VI, L.P.                            304,097          $6,050,500
         c/o The Prime Group, Inc.
         77 West Wacker Drive
         Suite 3900
         Chicago, IL 60601
         Attn:  Michael W. Reshcke
                Robert J. Rudnik

H Group LLC                                     133,050          $2,000,000
         c/o Heitman Financial Ltd.
         180 N. LaSalle
         Suite 3600
         Chicago, IL 60601
         Attn:  Norman Perlmutter
Ray R. Grinvalds                                  5,216            $104,320
         217 Deer Valley Drive
         Barrington, IL 60010

Warren H. John, as Trustee of the Warren         37,259            $745,180
H. John Trust dated December 18, 1998
         1730 N. Clark Street
         Chicago, IL 60614
</TABLE>


                                   EXHIBIT A-3
<PAGE>

<TABLE>
<CAPTION>
                                                  Number of              Capital
Managing General Partner                       Preferred Units        Contribution
------------------------                       ---------------        ------------
<S>                                   <C>                             <C>
Prime Group Realty Trust              2,000,000                          **
         77 West Wacker Drive         Convertible Preferred
                                      Units
         Suite 3900
         Chicago, IL  60601
         Attn:  Richard S. Curto
                James F. Hoffman

Prime Group Realty Trust              4,000,000                          **/
         77 West Wacker Drive         Series B Preferred                 --
                                      Units
         Suite 3900
         Chicago, IL  60601
         Attn:  Richard S. Curto
                James F. Hoffman
</TABLE>
-------------------------

** This amount shall be inserted by the Managing General Partner.

                                   EXHIBIT A-4