Document:

<PAGE>

                                                                    EXHIBIT 10.1

               AMENDMENT No. 1 TO REGISTRATION RIGHTS AGREEMENT
               ------------------------------------------------

     THIS AMENDMENT No. 1, dated as of August 18, 2001 (this "Amendment"), is
                                                              ---------
made by and among Kindred Healthcare, Inc. (formerly named Vencor, Inc.), a
Delaware corporation (the "Company"), and the holders identified on the
                           -------
signature pages hereto (the "Holders"), with respect to the Registration Rights
                             -------
Agreement, dated as of April 20, 2001 (the "Registration Rights Agreement"), by
                                            -----------------------------
and among the Company and the Holders.  For all purposes of this Amendment,
capitalized terms used but not defined herein have the meanings assigned to such
terms in the Registration Rights Agreement.

                                   RECITALS

     WHEREAS, the Company and the Holders have heretofore entered into the
Registration Rights Agreement;

     WHEREAS, the Company has informed the Holders that it desires, for valid
business reasons, a 30-day extension of the time for it to file a Shelf
Registration Statement in accordance with Section 2 of the Registration Rights
Agreement (the "Extension"); and
                ---------

     WHEREAS, the Company and the Holders are willing to enter into such
amendment;

     NOW, THEREFORE, for good and valuable consideration, the receipt and
adequacy of which are hereby acknowledged, it is agreed as follows:

                                   ARTICLE I

                                   AMENDMENT
                                   ---------

     Section 2(a) of the Registration Rights Agreement is hereby amended by
replacing the number "120" in the second line thereof with the number "150".

                                  ARTICLE II

                                 MISCELLANEOUS
                                 -------------

     Section 2.1.  Regarding the Company and the Holders.  All of the provisions
                   -------------------------------------
of the Registration Rights Agreement with respect to the rights and duties of
the Company and the Holders shall be applicable in respect hereof as fully and
with like effect as if set forth herein in full.  Each Holder is a party to the
Registration Rights Agreement and has not transferred or assigned any of its
rights thereunder to any other Person.

     Section 2.2.  Continuing Effect.  Except as expressly amended by this
                   -----------------
Amendment, the Registration Rights Agreement shall remain in full force and
effect in accordance with its terms.
<PAGE>

     Section 2.3.  References to Registration Rights Agreement.  All references
                   -------------------------------------------
to the Registration Rights Agreement in the Registration Rights Agreement or in
any other document executed or delivered in connection therewith shall, from and
after the effectiveness of this Amendment, be deemed to be references to the
Registration Rights Agreement as amended hereby, unless the context expressly
requires otherwise.

     Section 2.4.  Governing Law.  THIS AMENDMENT SHALL BE GOVERNED BY AND
                   -------------
CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE JURISDICTION WHICH GOVERN THE
REGISTRATION RIGHTS AGREEMENT AND ITS CONSTRUCTION.

     Section 2.5.  Counterparts.  This Amendment may be executed in any number
                   ------------
of counterparts, each of which so executed shall be deemed to be an original,
but all such counterparts shall together constitute but one and the same
instrument.

                            [Signature Pages Follow]

                                       2
<PAGE>

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

                                    KINDRED HEALTHCARE, INC.

                                    By:  /s/ Richard A. Schweinhart
                                         ---------------------------------------
                                         Name:  Richard A. Schweinhart
                                         Title: Senior Vice President & Chief
                                                Financial Officer

                                    HOLDERS:

                                    THE VENTAS STOCKHOLDER TRUST

                                    By:  The Bank of New York, not in its
                                         individual capacity, but solely as
                                         trustee

                                    By:  /s/ MaryBeth Lewicki
                                         ---------------------------------------
                                         Name:  MaryBeth Lewicki
                                         Title: Vice President

                                    VENTAS REALTY, LIMITED PARTNERSHIP

                                    By:  Ventas, Inc., its General Partner

                                    By:  /s/ T. Richard Riney
                                         ---------------------------------------
                                         Name:  T. Richard Riney
                                         Title: Executive Vice President and
                                                General Counsel

                                       3
<PAGE>

                                    FRANKLIN MUTUAL ADVISERS, LLC

                                    By:  /s/ Bradley Takahashi
                                         ---------------------------------------
                                         Name:  Bradley Takahashi
                                         Title: Assistant Vice President

                                    APPALOOSA MANAGEMENT L.P.,
                                    on behalf of certain accounts for which it
                                    acts as investment advisor

                                    By:  /s/ Ronald M. Goldstein
                                         ---------------------------------------
                                         Name:  Ronald M. Goldstein
                                         Title: Chief Financial Officer

                                    GOLDMAN SACHS & CO.

                                    By:  /s/ Dan Allen
                                         ---------------------------------------
                                         Name:  Dan Allen
                                         Title: Authorized Signatory

                                       4<PAGE>

                                                                    EXHIBIT 10.2

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

     THIS AMENDMENT No. 2, dated as of October 22, 2001 (this "Amendment"), is
                                                               ---------
made by and among Kindred Healthcare, Inc. (formerly named Vencor, Inc.), a
Delaware corporation (the "Company"), and the holders identified on the
                           -------
signature pages hereto (the "Holders"), with respect to the Registration Rights
                             -------
Agreement, dated as of April 20, 2001, by and among the Company and the Holders,
as amended by Amendment No. 1 to Registration Rights Agreement, dated as of
August 13, 2001, among the Company and the holders identified on the signature
pages thereto (as so amended, the "Registration Rights Agreement").  For all
                                   -----------------------------
purposes of this Amendment, capitalized terms used but not defined herein have
the meanings assigned to such terms in the Registration Rights Agreement.

                                   RECITALS

     WHEREAS, the Company and the Holders have heretofore entered into the
Registration Rights Agreement;

     WHEREAS, the Company has filed a Registration Statement on Form S-3
(Registration No. 333-68838) with the Commission on August 31, 2001 (the
"Underwritten Offering Registration Statement") with respect to an underwritten
offering of shares of its common stock (the "Underwritten Offering");

     WHEREAS, the Company has filed a Registration Statement on Form S-3
(Registration No. 333-69646) with the Commission on September 19, 2001 (the
"Shelf Registration Statement") pursuant to Section 2 of the Registration Rights
Agreement;

     WHEREAS, Ventas has notified the Company of its intent to exercise its
right under Section 4(a) of the Registration Rights Agreement to include certain
of its Registrable Securities in the Underwritten Offering Registration
Statement in order to, among other things, effect one or more Ventas Stockholder
Distributions;

     WHEREAS, for certain business reasons, the Company has requested that
Ventas waive its right under Section 4(a) of the Registration Rights Agreement
to effect a Ventas Stockholder Distribution pursuant to the Underwritten
Offering Registration Statement and instead effect any Ventas Stockholder
Distribution pursuant to the Shelf Registration Statement; and

     WHEREAS, Ventas is willing to accommodate the Company and waive its right
to effect a Ventas Stockholder Distribution pursuant to the Underwritten
Offering Registration Statement and instead effect any Ventas Stockholder
Distribution pursuant to the Shelf Registration Statement, as long as (i) the
Company and the other Holders waive certain provisions of the Registration
Rights Agreement so as to permit Ventas and Ventas, Inc. to effect a Ventas
Stockholder Distribution pursuant to the Shelf Registration Statement during the
Black-out Period (as defined below), (ii) any such Ventas Stockholder
Distribution is permissible under any underwriting agreement entered into by the
Company, the underwriters for the Underwritten Offering and the selling
stockholders electing to sell Registrable Securities in the Underwritten
Offering (the "Underwriting Agreement") and (iii) the Company takes all
necessary action to
<PAGE>

cause the Shelf Registration Statement and the Underwritten
Offering Registration Statement to be simultaneously declared effective by the
Commission;

     NOW, THEREFORE, for good and valuable consideration, the receipt and
adequacy of which are hereby acknowledged, it is agreed as follows:

                                   ARTICLE I

                                    WAIVER
                                    ------

Section 1.1.  Waiver.  The parties hereby agree that, if the black-out
              ------
provisions set forth in Section 5(a)(i) or (ii) of the Registration Rights
Agreement become operative due to the Underwritten Offering, such provisions
shall be waived solely to the extent they become so operative and solely to the
extent set forth in the Lock-Up Agreement to be executed by Ventas in favor of
the underwriters party to the Underwriting Agreement in connection with the
Underwritten Offering (the "Lock-Up Agreement"), in order to permit Ventas and
Ventas, Inc. to effect one or more Ventas Stockholder Distributions pursuant to
the Shelf Registration Statement; provided, however, that, during the black-out
period provided for in the Lock-Up Agreement (the "Black-out Period"), Ventas
and Ventas, Inc. may only effect a Ventas Stockholder Distribution in accordance
with the terms thereof.  The parties expressly agree that nothing contained
herein shall be deemed to limit the right of Ventas and Ventas, Inc. to effect a
Ventas Stockholder Distribution pursuant to the Shelf Registration Statement in
accordance with the terms of the Registration Rights Agreement after the
expiration of the Black-out Period.

                                  ARTICLE II

                          REPRESENTATION AND WARRANTY
                          ---------------------------

     Section 2.1.  Representation of the Holders.  Each Holder represents to the
                   -----------------------------
Company and each other Holder that it is a party to the Registration Rights
Agreement and has not transferred or assigned any of its rights thereunder to
any other Person.

                                  ARTICLE III

                                   COVENANTS
                                   ---------

     Section 3.1.  Effectiveness of Registration Statements.  The Company shall
                   ----------------------------------------
cause the Shelf Registration Statement and the Underwritten Offering
Registration Statement to be simultaneously declared effective by the
Commission.

                                  ARTICLE IV

                                 MISCELLANEOUS
                                 -------------

     Section 4.1.  Regarding the Company and the Holders.  All of the provisions
                   -------------------------------------
of the Registration Rights Agreement with respect to the rights and duties of
the Company and the

                                       2
<PAGE>

Holders shall be applicable in respect hereof as fully and with like effect as
if set forth herein in full.

     Section 4.2.  Continuing Effect.  Except as expressly amended by this
                   -----------------
Amendment, the Registration Rights Agreement shall remain in full force and
effect in accordance with its terms.

     Section 4.3.  References to Registration Rights Agreement.  All references
                   -------------------------------------------
to the Registration Rights Agreement in the Registration Rights Agreement or in
any other document executed or delivered in connection therewith shall, from and
after the effectiveness of this Amendment, be deemed to be references to the
Registration Rights Agreement as amended hereby, unless the context expressly
requires otherwise.

     Section 4.4.  Governing Law.  THIS AMENDMENT SHALL BE GOVERNED BY AND
                   -------------
CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE JURISDICTION WHICH GOVERN THE
REGISTRATION RIGHTS AGREEMENT AND ITS CONSTRUCTION.

     Section 4.5.  Counterparts.  This Amendment may be executed in any number
                   ------------
of counterparts, each of which so executed shall be deemed to be an original,
but all such counterparts shall together constitute but one and the same
instrument.

                            [Signature Pages Follow]

                                       3
<PAGE>

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

                                    KINDRED HEALTHCARE, INC.

                                    By:  /s/ Richard A. Lechleiter
                                         ---------------------------------------
                                         Name:  Richard A. Lechleiter
                                         Title: Vice President, Finance

                                    HOLDERS:

                                    THE VENTAS STOCKHOLDER TRUST

                                    By:  The Bank of New York, not in its
                                         individual capacity, but solely as
                                         trustee

                                    By:  /s/ MaryBeth Lewicki
                                         ---------------------------------------
                                         Name:  MaryBeth Lewicki
                                         Title: Vice President

                                    VENTAS REALTY, LIMITED PARTNERSHIP

                                    By:  Ventas, Inc., its General Partner

                                    By:  /s/ T. Richard Riney
                                         ---------------------------------------
                                         Name:  T. Richard Riney
                                         Title: Executive Vice President and
                                                General Counsel

                                       4
<PAGE>

                                    FRANKLIN MUTUAL ADVISERS, LLC

                                    By:  /s/ Bradley Takahashi
                                         ---------------------------------------
                                         Name:  Bradley Takahashi
                                         Title: Assistant Vice President

                                    APPALOOSA MANAGEMENT L.P.,
                                    on behalf of certain accounts for which it
                                    acts as investment advisor

                                    By:  /s/ James E. Bolin
                                         ---------------------------------------
                                         Name:  James E. Bolin
                                         Title: Vice President

                                    GOLDMAN SACHS & CO.

                                    By:  /s/ Stephen P. Hickey
                                         ---------------------------------------
                                         Name:  Stephen P. Hickey
                                         Title: Authorized Signatory

                                       5

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