<PAGE>
                                                                    EXHIBIT 10.2


                               FIRST AMENDMENT TO
               SECOND AMENDED AND RESTATED OPERATING AGREEMENT OF
                                  GGPLP L.L.C.

      THIS FIRST AMENDMENT (the "First Amendment") is made and entered into on
the 23rd day of April, 2002, by and among the undersigned parties.

                              W I T N E S S E T H:

      WHEREAS, a Delaware limited liability company known as GGPLP L.L.C. (the
"Company") exists pursuant to the Delaware Limited Liability Company Act and
that certain Second Amended and Restated Operating Agreement dated April 17,
2002, as amended (the "Restated Agreement"), among GGP Limited Partnership, a
Delaware limited partnership (the "Operating Partnership"), GGP American
Properties Inc., a Delaware corporation, Caledonian Holding Company, Inc., a
Delaware corporation, GSEP 2000 Realty Corp., a Delaware corporation (the "GS
2000 REIT"), GS 2002 Realty Corp., a Delaware corporation ("GS 2002 REIT"), and
General Growth Properties, Inc., a Delaware corporation ("GGPI");

      WHEREAS, GGPI has granted certain registration rights to the GS 2002 REIT
pursuant to that certain Registration Rights Agreement dated April 17, 2002 (the
"Registration Rights Agreement"), between the GS 2002 REIT and GGPI;

      WHEREAS, concurrently herewith, the GS 2002 REIT is contributing an
additional $10,000,000 to the capital of the Company and, in exchange therefor,
the Company is issuing to the GS 2002 REIT additional Series B Preferred Units
(as defined in the Restated Agreement); and

      WHEREAS, the parties hereto, being all of the members of the Company,
desire to amend the Restated Agreement to reflect such capital contribution and
issuance of Series B Preferred Units and to set forth certain understandings
among them.

      NOW, THEREFORE, in consideration of the mutual covenants and agreements
herein contained and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties hereto do hereby agree
as follows:

      1. CAPITALIZED TERMS. Capitalized terms used but not defined herein shall
have the definitions assigned to such terms in the Restated Agreement, as
amended hereby.

      2. AMENDMENT TO SECTION 1.1. Section 1.1 of the Restated Agreement is
hereby amended by deleting the last sentence of the definition of "Units" and
inserting the following in its place and stead:

      "The number and designation of all Units held by each Member as of April
      23, 2002 is set forth opposite such Member's name on Schedule A."
<PAGE>
      3. AMENDMENT TO SECTION 4.7. Section 4.7 of the Restated Agreement is
hereby amended by deleting the number "200,000" after the word "be" and before
the period in the seventh and eighth lines thereof and inserting the number
"240,000" in its place and stead.

      4. AMENDMENT TO SECTION 1 OF SCHEDULE B . Section 1 of Schedule B of the
Restated Agreement is hereby amended by deleting the number "200,000" after the
word "be" and before the period in the fourth line thereof and inserting the
number "240,000" in its place and stead.

      5. AMENDMENTS TO SECTIONS 7 AND 8 OF SCHEDULE B. Sections 7 and 8 of
Schedule B to the Restated Agreement are hereby amended by deleting the phrase
"April 17" each time it appears therein and substituting "April 23" in its place
and stead.

      6. AMENDMENT TO SIGNATURE PAGE. The first signature page of the Restated
Agreement is hereby amended by inserting the phrase "and Section 7 of Schedule
B" after the phrase "Section 4.3(g)" and before the comma in the first paragraph
thereof.

      7. AMENDMENT TO SECTION 4.3(c), ETC. The word "special" is hereby inserted
after the word "any" and before the word "right" in clause (iii) of the first
paragraph of Section 4.3(c) of the Restated Agreement, clause (c) of the first
paragraph of Section 3 of Schedule B to the Restated Agreement, clause (iii) of
Section IV(a) of Exhibit B to the Restated Agreement and Section 5.b of the
purchase agreements relating to the previous issuances of Series A Preferred
Units and/or Series B Preferred Units. The GS 2002 REIT hereby approves the same
change to the Certificate of Designations creating the Series G REIT Preferred
Shares.

      8. ISSUANCE OF ADDITIONAL SERIES B PREFERRED UNITS. Concurrently herewith,
the Company is issuing to the GS 2002 REIT 40,000 Series B Preferred Units in
exchange for a Capital Contribution by the GS 2002 REIT of $10,000,000. The GS
2002 REIT is hereby admitted as a Member in respect of such Series B Preferred
Units, and the GS 2002 REIT hereby agrees to be bound by the provisions of the
Restated Agreement, as the same is amended hereby and as the same may be amended
from time to time, with respect to such Series B Preferred Units. The reference
in the Registration Rights Agreement to "Units" shall be deemed to include the
Series B Preferred Units referred to in this Section 7.

      9. NEW SCHEDULE A. Schedule A to the Restated Agreement, identifying the
Members and the number and type of Units owned by them, is hereby deleted in its
entirety and the Schedule A in the form attached hereto is hereby inserted in
its place and stead.

      10. OTHER PROVISIONS UNAFFECTED. Except as expressly amended hereby, the
Restated Agreement shall remain in full force and effect in accordance with its
terms.

                  [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]


                                      -2-
<PAGE>
      IN WITNESS WHEREOF, the parties hereto have executed this First Amendment
(and GGPI has executed this First Amendment solely for the purpose of binding
itself under Section 4.3(g) of the Restated Agreement, as amended hereby,
Section 7 of Schedule B to the Restated Agreement, as amended hereby, and the
last sentence of Section 7 of this First Amendment) on the day and year first
above written.

                                        MANAGING MEMBER:

                                        GGP LIMITED PARTNERSHIP, a Delaware
                                        limited partnership

                                        By:  General Growth Properties, Inc., a
                                             Delaware corporation, its general
                                             partner


                                        By: /s/ Bernard Freibaum
                                            -------------------------------
                                            Name:  Bernard Freibaum
                                                   ------------------------
                                            Title: Executive Vice President
                                                   ------------------------

                                        110 North Wacker Drive
                                        Chicago, Illinois  60606
                                        Attention:  John Bucksbaum


                                        OTHER MEMBERS:

                                        CALEDONIAN HOLDING COMPANY, INC., a
                                        Delaware corporation

                                        By: /s/ Bernard Freibaum
                                            ------------------------------------
                                            Name:  Bernard Freibaum
                                                   -----------------------------
                                            Title: Vice President
                                                   -----------------------------
                                             110 North Wacker Drive
                                             Chicago, Illinois 60606
                                             Attention:  John Bucksbaum


                                      -3-
<PAGE>
                                        GGP AMERICAN PROPERTIES INC., a Delaware
                                        corporation

                                        By: /s/ Bernard Freibaum
                                            ------------------------------------
                                            Name:  Bernard Freibaum
                                                   -----------------------------
                                            Title: Vice President
                                                   -----------------------------

                                             110 North Wacker Drive
                                             Chicago, Illinois 60606
                                             Attention:  John Bucksbaum


                                        GSEP 2000 REALTY CORP.

                                        By: /s/ Eric Lane
                                            ------------------------------------
                                            Name:  Eric Lane
                                                   -----------------------------
                                            Title: President and CEO
                                                   -----------------------------

                                             c/o Goldman, Sachs & Co.
                                             One New York Plaza
                                             New York, New York 10004
                                             Attention:  Eric Lane

                                        GSEP 2002 REALTY CORP.

                                        By: /s/ Eric Lane
                                            ------------------------------------
                                            Name:  Eric Lane
                                                   -----------------------------
                                            Title: President and CEO
                                                   -----------------------------

                                             c/o Goldman, Sachs & Co.
                                             One New York Plaza, 40th Floor
                                             New York, New York 10004
                                             Attention:  Eric Lane


                                      -4-
<PAGE>
                                        GGPI:

                                        GENERAL GROWTH PROPERTIES, INC., a
                                        Delaware corporation

                                        By: /s/ Bernard Freibaum
                                            ------------------------------------
                                            Name:  Bernard Freibaum
                                                   -----------------------------
                                            Title: Executive Vice President
                                                   -----------------------------

                                             110 North Wacker Drive
                                             Chicago, Illinois 60606
                                             Attention:  John Bucksbaum


                                      -5-
<PAGE>
                                   SCHEDULE A

                                     MEMBERS

<TABLE>
<CAPTION>
             Member                     Common Units               Preferred Units
             ------                     ------------               ---------------
<S>                                     <C>                   <C>
GGP Limited Partnership                    911,000                        0

Caledonian Holding Company, Inc.            29,600                        0

GGP American Properties Inc.                58,500                        0

GSEP 2000 Realty Corp.                           0            700,000 Series A Preferred
                                                                        Units

GSEP 2002 Realty Corp.                           0            240,000 Series B Preferred
                                                                        Units
</TABLE>


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