<PAGE>
                                                                   Exhibit 4(b)



                AMENDMENT NO. 2 TO REGISTRATION RIGHTS AGREEMENT
                ------------------------------------------------


                  AMENDMENT NO. 2 TO REGISTRATION  RIGHTS AGREEMENT,  dated as
of July 1, 2003 (this  "Amendment"), by and between  TXU Corp., a Texas
corporation  (the  "Company")  and each of the  entities  listed on Schedule A
attached hereto (each, a "Holder" and collectively, "Holders").

                  WHEREAS, the Company and UXT Holdings LLC and UXT Intermediary
LLC (together, the "Initial Purchasers") have heretofore entered into a
Registration Rights Agreement, dated as of November 22, 2002, (the "Agreement";
capitalized terms used herein without definition having the meaning ascribed
thereto in the Agreement);

                  WHEREAS, on December 19, 2002 the Company and the Initial
Purchasers amended the Agreement
pursuant to an Amendment No. 1 To Registration Rights Agreement;

                  WHEREAS, on December 19, 2002, the Initial Purchasers, with
the consent of the Company and TXU Energy, transferred an aggregate of $250
million of the Notes to the Holders other than the Initial Purchasers;

                  WHEREAS, in connection with the above mentioned transfer the
Initial Purchasers assigned all of their rights and obligations under the
Agreement to such other Holders with respect to the transferred Notes;

                  WHEREAS, the Holders hold in the aggregate all of the
 outstanding Notes;

                  WHEREAS, pursuant to Section 2.04 of the Notes, on the date
hereof the Holders will exchange (the "Exchange") their Notes for a preferred
equity interest in the Company ("Class B Preferred Membership Interests") having
substantially identical economic and other terms as the Notes and otherwise in
form and substance satisfactory to the Holders; and

                  WHEREAS, in contemplation of the Exchange, the Company and the
Holders desire to further amend the Agreement.

                  NOW, THERETOFORE, in consideration of the premises and the
covenants hereinafter contained and for other good and valuable consideration,
the receipt and sufficiency of which are hereby acknowledged, and intending to
be legally bound hereby, it is agreed as follows:
<PAGE>

          1.     Effective Period. The definition of "Effective Period"
                 -----------------
contained in Section 1 of the Agreement is amended in its entirety to read as
follows:

                 "Effective Period" shall mean the period commencing with the
                 -----------------
effective date of the Shelf Registration Statement and ending on the date that
is 180 days from the date that the number of Registrable Securities is less than
ten percent (10%) of the initial amount of Registrable Securities; provided,
however, that, for purposes of Section 12 hereof and Section 9 of the Exchange
Agreement, "Effective Period" shall mean the period ending on the date that the
Purchasers and their Affiliates, as a group, own Class B Preferred Membership
Interests and Common Stock aggregating less than $75,000,000 in aggregate unpaid
liquidation value (determined, in the case of Common Stock, on the basis of the
Class B Preferred Membership Interest Exercise Price at the date Exchange Rights
are exercised with respect to such Common Stock (as such terms are defined in
the Exchange Agreement)).

          2.     "Registrable Securities" The definition of "Registrable
                 ------------------------
Securities" shall be amended by replacing the term "Notes" with the term
"Class B Preferred Membership Interests".

          3.     Added Definitions. The following definitions shall be added
                 -----------------
in their entirety to Section 1 of the Agreement.

                 "Class B Preferred Membership Interests" shall have the
                 ----------------------------------------
meaning set forth in the LLC Agreement.

                "Exchange Agreement" means the Exchange Agreement, dated as of
                --------------------
November 22, 2002, among the Company, TXU Corp., UXT Intermediary LLC and UXT
Holdings LLC, as amended by Amendment No. 1 to the Exchange Agreement, dated as
of the date hereof, by and among the Company, TXU Corp. and the entities listed
on Schedule A thereto, and as the same may be further amended from time to time
in accordance with the terms thereof.

                "LLC Agreement" means the Company's Second Amended and
                ---------------
Restated Limited Liability Company Agreement dated as of July 1, 2003, as the
same may be amended from time to time in accordance with the terms thereof.

          4.    Amended Sections. (a) Sections 15(a), 15(e)(ii) and 15(e)
                ----------------
(iii) of the Agreement shall be amended by replacing in all instances the term
"Notes" with the term "Class B Preferred Membership Interests".

                (b) Section 15(d)(i) of the Agreement shall be amended by
replacing "Shearman & Sterling" with "Shearman & Sterling LLP".

          5.   Other Amendments. All references to the "Agreement" in the
               ----------------
Agreement shall, from and after the date hereof, be deemed to refer to the
Agreement as amended by this Amendment.

          6. Provisions of Agreement Not Otherwise Modified. Except as
             ----------------------------------------------
specifically amended by this Amendment, the Agreement is hereby ratified,
approved and confirmed and remains in full force and effect.


                                       2
<PAGE>

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


                                TXU CORP.



                                By:
                                   -----------------------------------------
                                Name: Kirk R. Oliver
                                Title:  Treasurer


                                UXT HOLDINGS LLC

                                By: DLJ Merchant Banking III, Inc. as Managing
                                Member

                                By:
                                   ----------------------------------------
                                Name:  Michael S. Isikow
                                Title: Principal


                                UXT INTERMEDIARY LLC

                                By: UXT AIV, L.P., its Managing Member

                                By: DLJ Merchant Banking III, Inc., as Managing
                                General Partner

                                By:
                                   --------------------------------------------
                                Name:  Michael S. Isikow
                                Title: Principal


                                BENJAMIN MOORE PENSION


                                By:--------------------------------------------
                                Name:  Mark D. Millard
                                Title: Authorized Signatory



                                       3
<PAGE>


                                THE BUFFALO NEWS OFFICE PENSION PLAN


                                By:------------------------------------------
                                Name:  Mark D. Millard
                                Title:  Authorized Signatory


                                THE BUFFALO NEWS EDITORIAL PENSION
                                PLAN


                                By:-----------------------------------------
                                Name:  Mark D. Millard
                                Title: Authorized Signatory


                                CORNHUSKER CASUALTY COMPANY


                                By:-----------------------------------------
                                Name:  Mark D. Millard
                                Title: Authorized Signatory


                                FLIGHTSAFETY INTERNATIONAL INC.
                                RETIREMENT INCOME PLAN


                                By:-----------------------------------------
                                Name:  Mark D. Millard
                                Title: Authorized Signatory


                                FRUIT OF THE LOOM PENSION TRUST


                                By:-----------------------------------------
                                Name:  Mark D. Millard
                                Title: Authorized Signatory




                                       4
<PAGE>


                                GEICO CORPORATION PENSION PLAN
                                TRUST


                                By:-------------------------------------------
                                Name:   Mark D. Millard
                                Title:  Authorized Signatory


                                GOVERNMENT EMPLOYEES INSURANCE
                                COMPANY


                                By:------------------------------------------
                                Name:  Mark D. Millard
                                Title:  Authorized Signatory


                                JOHNS MANVILLE CORPORATION MASTER
                                PENSION TRUST


                                By:-----------------------------------------
                                Name:  Mark D. Millard
                                Title: Authorized Signatory


                                JUSTIN BRANDS, INC. UNION PENSION PLAN
                                AND JUSTIN BRANDS, INC. PENSION PLAN &
                                TRUST


                                By:----------------------------------------
                                Name:  Mark D. Millard
                                Title: Authorized Signatory


                                ACME BRICK COMPANY PENSION TRUST


                                By:-----------------------------------------
                                Name:  Mark D. Millard
                                Title: Authorized Signatory



                                       5
<PAGE>

                                SCOTT FETZER COMPANY COLLECTIVE
                                INVESTMENT TRUST


                                By:-----------------------------------------
                                Name:  Mark D. Millard
                                Title: Authorized Signatory





                                       6
<PAGE>


                                                                  Schedule A
                                                                  ----------



         UXT Intermediary LLC

         UXT Holdings LLC

         Benjamin Moore Pension

         Buffalo News Office Pension Plan

         Buffalo News Editorial Pension Plan

         Cornhusker Casualty Company

         FlightSafety International Inc. Retirement Income Plan

         Fruit of the Loom Pension Trust

         GEICO Corporation Pension Plan Trust

         Government Employees Insurance Company

         Johns Manville Corporation Master Pension Trust

         Justin Brands, Inc. Union Pension Plan and Justin Brands, Inc.
              Pension Plan and Trust

         Acme Brick Company Pension Trust

         Scott Fetzer Company Collective Investment Trust


                                       7
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