<PAGE>
 
                                EXHIBIT 10(DD)

                                      TO

                                   FORM 10-K

                                      OF

                        WELLS REAL ESTATE FUND X, L.P.

                                    FOR THE

                      FISCAL YEAR ENDED DECEMBER 31, 1998
<PAGE>
 
                  FIRST AMENDMENT TO JOINT VENTURE AGREEMENT
                                      OF
                        WELLS/ORANGE COUNTY ASSOCIATES


     THIS FIRST AMENDMENT TO JOINT VENTURE AGREEMENT OF WELLS/ORANGE COUNTY
ASSOCIATES (the "First Amendment") is made and entered into as of the 1st day of
September, 1998, by and among WELLS OPERATING PARTNERSHIP, L.P., a Delaware
limited partnership having Wells Real Estate Investment Trust, Inc. as general
partner ("Wells OP"), as Venturer, WELLS DEVELOPMENT CORPORATION, a Georgia
corporation ("Wells Development"), as withdrawing Venturer, and FUND X AND FUND
XI ASSOCIATES, a Georgia joint venture comprised of Wells Real Estate Fund X,
L.P. and Wells Real Estate Fund XI, L.P. (the "Fund X-XI Joint Venture"), as a
newly admitted Venturer to WELLS/ORANGE COUNTY ASSOCIATES (the "Venture").

                             W I T N E S S E T H :

     WHEREAS, Wells OP and Wells Development have previously formed the Venture
pursuant to the terms and provisions of that certain Joint Venture Agreement of
Wells/Orange County Associates dated July 27, 1998 (the "Joint Venture
Agreement"); and

     WHEREAS, Wells Development has, simultaneously herewith, transferred and
assigned all of its right, title and interest in and to its interest in the
Joint Venture to the Fund X-XI Joint Venture; and

     WHEREAS, the parties hereto desire to amend the Joint Venture Agreement to
reflect the transfer and assignment by Wells Development of its interest in the
Venture to the Fund X-XI Joint Venture and to implement and effect the admission
of the Fund X-XI Joint Venture to the Venture as a Venturer in the place of
Wells Development and the withdrawal of Wells Development from the Venture.

     NOW, THEREFORE, in consideration of the mutual covenants and conditions
hereinafter set forth, and for other good and valuable consideration, the
receipt and sufficiency of which is hereby acknowledged, the parties hereto
hereby agree, and the Joint Venture Agreement is hereby amended, as follows:


                           Admission and Withdrawal
                           ------------------------

     Fund X and Fund XI Associates, a Georgia joint venture comprised of Wells
Real Estate Fund X, L.P. and Wells Real Estate Fund XI, L.P. (the "Fund X-XI
Joint Venture") is hereby admitted to the Venture in the place of Wells
Development.  By its execution hereof, the Fund X-XI Joint Venture hereby adopts
and agrees to be bound by the terms of the Joint Venture Agreement.  The Fund X-
XI Joint Venture hereby further, without limitation of the foregoing, 
<PAGE>
 
adopts, ratifies and confirms the provisions of Sections 6.4(d) and 6.5(e) of
the Joint Venture Agreement and the appointment of the Accepting Venturer, as
defined in the Joint Venture Agreement, as its attorney-in-fact for the purposes
and to the extent therein set forth.

     By its execution hereof, Wells OP hereby consents to the transfer of by
Wells Development of its interest in the Venture to the Fund X-XI Joint Venture
and the admission of the Fund X-XI Joint Venture to the Venture pursuant to the
terms and provisions of this First Amendment.

     Wells Development Corporation hereby withdraws from the Venture and agrees
that, subsequent to the date hereof, it shall have no further right, title or
interest in or to any profits, losses, income, gain, Net Cash Flow,
Extraordinary Receipts or capital of the Venture, and no further rights, powers
or authority as a Venturer in the Venture.


                           Amendment to Section 3.1
                           ------------------------

     Section 3.1 of the Joint Venture Agreement is hereby amended and restated
in its entirety as follows:

         "3.1  Capital Contributions.  It is hereby acknowledged and agreed that
               ---------------------                                            
     the Venturers have made the following Capital Contributions to the Venture
     and own the following Distribution Percentage Interests in the Venture,
     effective September 1, 1998:

 
                                                         Distribution
                                              Capital     Percentage
                 Venturer                   Contribution   Interest
                 --------                   ------------  ----------
 
                 Wells OP                     $2,861,874      44%
                 Fund X-XI Joint Venture      $3,695,000      56%
                                              ----------     ----
                   Total                      $6,556,874     100%
 

     The Venturers shall, from time to time, make such further Capital
     Contributions to the Venture in such amounts as are mutually agreed to by
     the Venturers."
<PAGE>
 
                           Amendment to Section 8.1
                           ------------------------

     Section 8.1 of the Joint Venture Agreement is hereby amended by deleting
reference to "Wells Development Corporation" and inserting in lieu thereof the
following address of the Fund X-XI Joint Venture:

                         Fund X and Fund XI Associates
                           3885 Holcomb Bridge Road
                            Norcross, Georgia 30092


                                RECERTIFICATION
                                ---------------

     Wells OP and the Fund X-XI Joint Venture hereby adopt, ratify and recertify
the Joint Venture Agreement, except as specifically amended hereby, and the
Joint Venture Agreement shall continue and remain in full force and effect.

     IN WITNESS WHEREOF, the undersigned have executed this First Amendment to
Joint Venture Agreement of Wells/Orange County Associates under seal as of the
day and year first above written.

                               WELLS OP:
                               -------- 

                               WELLS OPERATING PARTNERSHIP, L.P.
                               A Delaware Limited Partnership

                               By:  Wells Real Estate Investment Trust, Inc.
Signed, sealed and delivered   A Maryland Corporation
in the presence of:                 (As General Partner)


/s/ Judith A. Miller                     By: /s/ Leo F. Wells, III
--------------------                         ---------------------
Unofficial Witness                           Leo F. Wells, III
                                             President

/s/ Martha Jean Cory
--------------------
Notary Public

[Notarial Seal]
<PAGE>
 
                                WITHDRAWING VENTURER:
                                -------------------- 

Signed, sealed and delivered    WELLS DEVELOPMENT CORPORATION
in the presence of:             A Georgia Corporation


/s/ Judith A. Miller            By: /s/ Leo F. Wells, III
--------------------               ----------------------
Unofficial Witness                  Leo F. Wells, III
                                    President

/s/ Martha Jean Cory
--------------------
Notary Public

[Notarial Seal]
<PAGE>
 
                               NEWLY ADMITTED VENTURER:
                               ----------------------- 

                               FUND X AND FUND XI ASSOCIATES
                               A Georgia Joint Venture

                               By:  Wells Real Estate Fund X, L.P.
                                    A Georgia Limited Partnership

                                    By:  Wells Partners, L.P.
                                         A Georgia Limited Partnership
                                         (As General Partner)

                                    By:  Wells Capital, Inc.
Signed, sealed and delivered             A Georgia Corporation
in the presence of:                      (As General Partner)


/s/ Judith A. Miller                By: /s/ Leo F. Wells, III
--------------------                    ----------------------
Unofficial Witness                      Leo F. Wells, III
                                        President

/s/ Martha Jean Cory
--------------------
Notary Public

[Notarial Seal]


Signed, sealed and delivered
in the presence of:


/s/ Judith A. Miller                By: /s/ Leo F. Wells, III
--------------------                    ---------------------
Unofficial Witness                      Leo F. Wells, III
                                        (As General Partner)

/s/ Martha Jean Cory
--------------------
Notary Public

[Notarial Seal]
<PAGE>
 
                               By:  Wells Real Estate Fund XI, L.P.
                                    A Georgia Limited Partnership

                                    By:  Wells Partners, L.P.
                                         A Georgia Limited Partnership
                                         (As General Partner)

                                         By:  Wells Capital, Inc.
Signed, sealed and delivered             A Georgia Corporation
in the presence of:                           (As General Partner)


/s/ Judith A. Miller                     By: /s/ Leo F. Wells, III
--------------------                        ----------------------
Unofficial Witness                          Leo F. Wells, III
                                            President

/s/ Martha Jean Cory
--------------------
Notary Public

[Notarial Seal]


Signed, sealed and delivered
in the presence of:


/s/ Judith A. Miller                      By:/s/ Leo F. Wells, III
--------------------                         ---------------------
Unofficial Witness                           Leo F. Wells, III
                                             (As General Partner)

/s/ Martha Jean Cory
--------------------
Notary Public

[Notarial Seal]