Document:

<PAGE>   1

                                                                     EXHIBIT 4.6

================================================================================

                            TELE-COMMUNICATIONS, INC.

                                       and

                          THE BANK OF NEW YORK, Trustee

                                ----------------

                          SECOND SUPPLEMENTAL INDENTURE
                          Dated as of February 25, 2000

              Supplement to Indenture Dated as of February 19, 1998
                               as supplemented by
             First Supplemental Indenture Dated as of March 9, 1999

                              --------------------

                          7.125% Senior Notes due 2028
                          6.375% Senior Notes due 2003

================================================================================

<PAGE>   2

     THIS SECOND SUPPLEMENTAL INDENTURE (this "Supplemental Indenture") is made
as of February 25, 2000, between TELE-COMMUNICATIONS, INC., a Delaware
corporation ("TCI" or, the "Company"), as successor issuer, and THE BANK OF NEW
YORK, a New York banking corporation (the "Trustee"), as trustee.

                                    RECITALS

     WHEREAS, TCI and the Trustee are parties to an Indenture, dated as of
February 19, 1998, as supplemented by a First Supplemental Indenture, dated as
of March 9, 1999 (collectively, the "Original Indenture"), pursuant to which the
Company issued (as successor issuer), and the Trustee authenticated and
delivered the following securities which are, as of the date hereof, currently
outstanding (collectively, the "Securities"):

(a) $300,000,000 aggregate principal amount of the Company's 7.125% Senior Notes
due 2028; and

(b) $750,000,000 aggregate principal amount of the Company's 6.375% Senior Notes
due 2003;

     WHEREAS, the Board of Directors of TCI has determined that it is in the
best interests of TCI to convert its corporate form from a Delaware corporation
to a Delaware limited liability company pursuant to Section 266 of the Delaware
General Corporation Law and Section 18-214 of the Delaware Limited Liability
Company Act (the "Conversion");

     WHEREAS, the Board of Directors of TCI has determined that it is advisable
to amend certain provisions of the Original Indenture which may affect the
Conversion;

     WHEREAS, the Original Indenture provides that the Company and the Trustee
may amend or supplement the Original Indenture or the Securities of any series
without notice to or consent of any Holder of Securities or coupons to make any
change that, in the opinion of the Board of Directors, does not materially
adversely affect the rights of any Securityholder or the Holder of any coupon;

     WHEREAS, the Board of Directors of TCI has determined that the amendments
to the Indenture contained in this Supplemental Indenture do not materially
adversely affect the rights of any Securityholder or the Holder of any coupon;
and

     WHEREAS, this Supplemental Indenture has been duly authorized by all
necessary action on the part of TCI.

     NOW, THEREFORE, TCI and the Trustee agree as follows for the equal and
ratable benefit of the Holders:

                                      -1-
<PAGE>   3

                                    ARTICLE I

                           DEFINITIONS; INTERPRETATION

SECTION 1.1         Definitions. Capitalized terms that are defined in the
               preamble or the recitals hereto shall have such meanings
               throughout this Supplemental Indenture. Capitalized terms used
               but not defined in this Supplemental Indenture have the meanings
               assigned thereto in the Original Indenture. The meanings assigned
               to all defined terms used in this Supplemental Indenture shall be
               equally applicable to both the singular and plural forms of such
               defined terms. The term "Indenture" as used herein means the
               Original Indenture, as amended and supplemented by this
               Supplemental Indenture, or as otherwise supplemented or amended
               from time to time by one or more indentures supplemental thereto
               or hereto entered into pursuant to the applicable provisions of
               the Indenture.

SECTION 1.2         Interpretation. References in the Original Indenture
               (including references in the Original Indenture as amended or
               supplemented hereby) to "this Indenture" (and indirect references
               such as "hereunder," "herein" and "hereof") shall be deemed
               references to the Original Indenture as amended and supplemented
               hereby. All of the covenants, agreements and provisions of this
               Supplemental Indenture shall be deemed to be and construed as
               part of the Original Indenture to the same effect as if fully set
               forth therein and shall be fully enforceable in the manner
               provided in the Original Indenture. Except as otherwise provided
               in this Supplemental Indenture, all of the covenants, agreements
               and provisions of the Original Indenture shall remain in full
               force and effect.

                                   ARTICLE II

                                   AMENDMENTS

SECTION 2.1         Amendments. The following provisions of the Original
               Indenture are hereby amended, modified, supplemented or replaced
               as follows:

     (a)            The definition of "Board of Directors" contained in Article
               One, Section 1.01 of the Original Indenture is amended to read in
               its entirety as follows: "Board of Directors means the Board of
               Directors of the Company or any authorized committee thereof, or,
               if the Company is not a corporation, the equivalent decision
               making body thereof or authorized committee thereof."

                                      -2-
<PAGE>   4

     (b)            The definition of "Officer" contained in Article One,
               Section 1.01 of the Original Indenture is amended to add the
               words "(if any)" after the words "Chairman of the Board."

     (c)            Article Four, Section 4.07 is hereby amended to replace the
               word "corporate" appearing in the heading to such section and as
               the second to the last word of such section with the word
               "legal."

     (d)            Article Five is hereby amended to replace the word
               "CORPORATION" appearing in the heading thereof with the word
               "ENTITY."

     (e)            Article Five, Section 5.01 is hereby amended to insert the
               words "or limited liability company" after each occurrence of the
               word "corporation."

     (f)            Article Five, Section 5.01 is also hereby amended to insert
               the following words as a new paragraph after the first paragraph
               thereof: "Nothing in this Indenture shall prohibit the Company
               from effecting a conversion pursuant to applicable law of the
               Company from a corporation into a limited liability company or
               from a limited liability company into a corporation, and any such
               conversion shall not be deemed to be a consolidation, merger or
               transfer subject to the requirements of the immediately preceding
               paragraph, provided, that such conversion by law shall not be
               deemed to affect any obligations or liabilities of the Company
               incurred prior to such conversion (including obligations or
               liabilities with respect to the Securities). Notice of any such
               conversion shall be promptly delivered to the Trustee."

     (g)            Article Ten, Section 10.15 is hereby amended to insert the
               words "or limited liability company" after the word "corporation"
               in clause (2) thereof.

                                   ARTICLE III

                                  MISCELLANEOUS

SECTION 3.1         Conflict with the TIA. If any provision of this Supplemental
               Indenture modifies or excludes any provision of the TIA that is
               required under such Act to be part of and govern the Indenture,
               the latter provision of the TIA shall control. If any provision
               hereof modifies or excludes any provision of the TIA that may be
               so modified or excluded, the latter provision

                                      -3-
<PAGE>   5

               of the TIA shall be deemed to apply to this Supplemental
               Indenture, as so modified or excluded, as the case may be.

SECTION 3.2         Date and Time of Effectiveness. This Supplemental Indenture
               shall become a legally effective and binding instrument at and as
               of the date hereof.

SECTION 3.3         Securities Deemed Conformed. As of the date hereof, the
               provisions of each Security then outstanding shall be deemed to
               be conformed, without the necessity for any reissuance or
               exchange of such Security or any other action on the part of the
               Holders, TCI or the Trustee, so as to reflect this Supplemental
               Indenture.

SECTION 3.4         Successors. All agreements of TCI and the Trustee in this
               Supplemental Indenture and in the Indenture shall bind their
               respective successors.

SECTION 3.5         Benefits of Supplemental Indenture. Nothing in this
               Supplemental Indenture, express or implied, shall give to any
               person, other than the parties hereto and their successors
               hereunder, any Agent, Authenticating Agent and the Holders, any
               benefit or any legal or equitable right, remedy or claim under
               this Supplemental Indenture or the Indenture.

SECTION 3.6         Separability. In case any provision in this Supplemental
               Indenture, or in the Indenture, shall be invalid, illegal or
               unenforceable, the validity, legality and enforceability of the
               remaining provisions shall not in any way be affected or impaired
               thereby, it being intended that all of the provisions hereof
               shall be enforceable to the full extent permitted by law.

SECTION 3.7         Trustee Responsibility. The Trustee assumes no duties,
               responsibilities or liabilities by reason of this Supplemental
               Indenture other than as set forth in the Original Indenture. The
               Trustee assumes no responsibility for the correctness of the
               statements herein contained, which shall be taken as statements
               of TCI. This Supplemental Indenture is executed and accepted by
               the Trustee subject to all of the terms and conditions of its
               acceptance of the trust under the Original Indenture, as fully as
               if said terms and conditions were herein set forth in full.

SECTION 3.8         Headings. The Article and Section headings of this
               Supplemental Indenture have been inserted for convenience of
               reference only, are not to be considered a part of this
               Supplemental Indenture and shall in no way modify or restrict any
               of the terms or provisions hereof.

                                      -4-
<PAGE>   6

SECTION 3.9         Counterparts. This Supplemental Indenture may be executed in
               counterparts, each of which shall for all purposes be deemed to
               be an original, and all such counterparts shall together
               constitute but one and the same instrument.

SECTION 3.10        Notices. The addresses for notices to the Company and the
               Trustee set forth in Section 11.02 of the Original Indenture
               shall be amended, without further action, to read in their
               entirety as follows:

               "If to the Company:

                       Tele-Communications, Inc.
                       9197 South Peoria Street
                       Englewood, Colorado 80112
                       Attention: Treasurer

               If to the Trustee:

                      The Bank of New York
                      101 Barclay Street, Floor 21W
                      New York, New York 10286"

SECTION 3.11        Governing Law. This Supplemental Indenture shall be governed
               by and construed in accordance with the internal laws of the
               State of New York.

                                      -5-
<PAGE>   7

     IN WITNESS WHEREOF, the parties hereto have caused this Supplemental
Indenture to be duly executed as of the day and year first above written.

                                             TELE-COMMUNICATIONS, INC.

                                             By:
                                                --------------------------------
                                                 Name:
                                                 Title:

                                             THE BANK OF NEW YORK, as Trustee

                                             By:
                                                --------------------------------
                                                 Name:
                                                 Title:

                                      -6-<PAGE>   1
                                                                     EXHIBIT 4.7

===============================================================================

                            TELE-COMMUNICATIONS, INC.

                                       and

                  STATE STREET BANK AND TRUST COMPANY, Trustee

                               ------------------

                          THIRD SUPPLEMENTAL INDENTURE
                          Dated as of February 25, 2000

                Supplement to Indenture Dated as of July 26, 1993
                               as supplemented by
         First Supplemental Indenture Dated as of September 13, 1994 and
             Second Supplemental Indenture Dated as of March 9, 1999

                               ------------------

                          7.250% Senior Notes due 2005
                        7.875% Senior Debentures due 2013
                          8.650% Senior Notes due 2004
                          8.000% Senior Notes due 2005
                        8.750% Senior Debentures due 2015

===============================================================================

<PAGE>   2

         THIS THIRD SUPPLEMENTAL INDENTURE (this "Supplemental Indenture") is
made as of February 25, 2000, between TELE-COMMUNICATIONS, INC., a Delaware
corporation ("TCI" or the "Company"), as successor issuer, and STATE STREET BANK
AND TRUST COMPANY, a Massachusetts Trust Company (the "Trustee"), as trustee.

                                    RECITALS

         WHEREAS, TCI and the Trustee (as successor trustee to Shawmut Bank
Connecticut, National Association ("Shawmut")), are parties to an Indenture,
dated as of July 26, 1993, as supplemented by the First Supplemental Indenture,
dated as of September 13, 1994, and the Second Supplemental Indenture, dated as
of March 9, 1999 (together, the "Original Indenture"), pursuant to which the
Company issued, and Shawmut authenticated and delivered the following securities
which are, as of the date hereof, currently outstanding (collectively, the
"Securities"):

(a) $300 million aggregate principal amount of the Company's 7.250% Senior Notes
    due 2005;

(b) $550 million aggregate principal amount of the Company's 7.875% Senior
    Debentures due 2013;

(c) $300 million aggregate principal amount of the Company's 8.650% Senior Notes
    due 2004;

(d) $350 million aggregate principal amount of the Company's 8.000% Senior Notes
    due 2005; and

(e) $750 million aggregate principal amount of the Company's 8.750% Senior
    Debentures due 2015;

         WHEREAS, the Board of Directors of TCI has determined that it is in the
best interests of TCI to convert its corporate form from a Delaware corporation
to a Delaware limited liability company pursuant to Section 266 of the Delaware
General Corporation Law and Section 18-214 of the Delaware Limited Liability
Company Act (the "Conversion");

         WHEREAS, the Board of Directors of TCI has determined that it is
advisable to amend certain provisions of the Original Indenture which may affect
the Conversion;

         WHEREAS, the Original Indenture provides that the Company and the
Trustee may amend or supplement the Original Indenture or the Securities of any
series without notice to or consent of any Holder of Securities or coupons to
make any change that, in the opinion of the Board of Directors, does not
materially adversely affect the rights of any Securityholder or the Holder of
any coupon;

         WHEREAS, the Board of Directors of TCI has determined that the
amendments to the Indenture contained in this Supplemental Indenture do not
materially adversely affect the rights of any Securityholder or the Holder of
any coupon; and

         WHEREAS, this Supplemental Indenture has been duly authorized by all
necessary action on the part of TCI.

                                      - 1 -

<PAGE>   3

         NOW, THEREFORE, TCI and the Trustee agree as follows for the equal and
ratable benefit of the Holders:

                                    ARTICLE I

                           DEFINITIONS; INTERPRETATION

         SECTION 1.01 Definitions. Capitalized terms that are defined in the
preamble or the recitals hereto shall have such meanings throughout this
Supplemental Indenture. Capitalized terms used but not defined in this
Supplemental Indenture have the meanings assigned thereto in the Original
Indenture. The meanings assigned to all defined terms used in this Supplemental
Indenture shall be equally applicable to both the singular and plural forms of
such defined terms. The term "Indenture" as used herein means the Original
Indenture, as amended and supplemented by this Supplemental Indenture, or as
otherwise supplemented or amended from time to time by one or more indentures
supplemental thereto or hereto entered into pursuant to the applicable
provisions of the Indenture.

         SECTION 1.02 Interpretation. References in the Original Indenture
(including references in the Original Indenture as amended or supplemented
hereby) to "this Indenture" (and indirect references such as "hereunder,"
"herein" and "hereof") shall be deemed references to the Original Indenture as
amended and supplemented hereby. All of the covenants, agreements and provisions
of this Supplemental Indenture shall be deemed to be and construed as part of
the Original Indenture to the same effect as if fully set forth therein and
shall be fully enforceable in the manner provided in the Original Indenture.
Except as otherwise provided in this Supplemental Indenture, all of the
covenants, agreements and provisions of the Original Indenture shall remain in
full force and effect.

                                   ARTICLE II

                                   AMENDMENTS

         SECTION 2.01 Amendments. The following provisions of the Original
Indenture are hereby amended, modified, supplemented or replaced as follows:

                  (a) The definition of "Board of Directors" contained in
         Article One, Section 1.01 of the Original Indenture is amended to read
         in its entirety as follows: "Board of Directors means the Board of
         Directors of the Company or any authorized committee thereof, or, if
         the Company is not a corporation, the equivalent decision making body
         thereof or authorized committee thereof."

                                      - 2 -

<PAGE>   4

                  (b) The definition of "Officer" contained in Article One,
         Section 1.01 of the Original Indenture is amended to add the words "(if
         any)" after the words "Chairman of the Board."

                  (c) The definition of "Subsidiary" contained in Article One,
         Section 1.01 of the Original Indenture is amended to add the words ",
         partnership, limited liability company, association or other business
         entity" after the occurrence of the word "corporation", to add the
         words "(or other voting securities)" after each occurrence of the words
         "voting stock", and to add the words "(or other securities)" after the
         words "capital stock."

                  (d) Article Four, Section 4.08 is hereby amended to replace
         the word "corporate" appearing in the heading to such section and as
         the second to the last word of such section with the word "legal."

                  (e) Article Five is hereby amended to replace the word
         "CORPORATION" appearing in the heading thereof with the word "ENTITY."

                  (f) Article Five, Section 5.01 is hereby amended to insert the
         words "or limited liability company" after each occurrence of the word
         "corporation."

                  (g) Article Five, Section 5.01 is also hereby amended to
         insert the following words as a new paragraph after the first paragraph
         thereof: "Nothing in this Indenture shall prohibit the Company from
         effecting a conversion pursuant to applicable law of the Company from a
         corporation into a limited liability company or from a limited
         liability company into a corporation, and any such conversion shall not
         be deemed to be a consolidation, merger or transfer subject to the
         requirements of the immediately preceding paragraph, provided, that
         such conversion by law shall not be deemed to affect any obligations or
         liabilities of the Company incurred prior to such conversion (including
         obligations or liabilities with respect to the Securities). Notice of
         any such conversion shall be promptly delivered to the Trustee."

                  (h) Article Ten, Section 10.15 is hereby amended to insert the
         words "or limited liability company" after the word "corporation" in
         clause (2) thereof.

                  (i) Article Ten, Section 10.16 is hereby amended to insert the
         words "or limited liability company" after each occurrence of the word
         "corporation."

                                      - 3 -

<PAGE>   5

                                   ARTICLE III

                                  MISCELLANEOUS

         SECTION 3.01 Conflict with the TIA. If any provision of this
Supplemental Indenture modifies or excludes any provision of the TIA that is
required under such Act to be part of and govern the Indenture, the latter
provision of the TIA shall control. If any provision hereof modifies or excludes
any provision of the TIA that may be so modified or excluded, the latter
provision of the TIA shall be deemed to apply to this Supplemental Indenture, as
so modified or excluded, as the case may be.

         SECTION 3.02 Date and Time of Effectiveness. This Supplemental
Indenture shall become a legally effective and binding instrument at and as of
the date hereof.

         SECTION 3.03 Securities Deemed Conformed. As of the date hereof, the
provisions of each Security then outstanding shall be deemed to be conformed,
without the necessity for any reissuance or exchange of such Security or any
other action on the part of the Holders, TCI or the Trustee, so as to reflect
this Supplemental Indenture.

         SECTION 3.04 Successors. All agreements of TCI and the Trustee in this
Supplemental Indenture and in the Indenture shall bind their respective
successors.

         SECTION 3.05 Benefits of Supplemental Indenture. Nothing in this
Supplemental Indenture, express or implied, shall give to any person, other than
the parties hereto and their successors hereunder, any Agent and the Holders,
any benefit or any legal or equitable right, remedy or claim under this
Supplemental Indenture or the Indenture.

         SECTION 3.06 Separability. In case any provision in this Supplemental
Indenture, or in the Indenture, shall be invalid, illegal or unenforceable, the
validity, legality and enforceability of the remaining provisions shall not in
any way be affected or impaired thereby, it being intended that all of the
provisions hereof shall be enforceable to the full extent permitted by law.

         SECTION 3.07 Trustee Responsibility. The Trustee assumes no duties,
responsibilities or liabilities by reason of this Supplemental Indenture other
than as set forth in the Original Indenture. The Trustee assumes no
responsibility for the correctness of the statements herein contained, which
shall be taken as statements of TCI. This Supplemental Indenture is executed and
accepted by the Trustee subject to all of the terms and conditions of its
acceptance of the trust under the Original Indenture, as fully as if said terms
and conditions were herein set forth in full.

         SECTION 3.08 Headings. The Article and Section headings of this
Supplemental Indenture have been inserted for convenience of reference only, are
not to be considered a part of this Supplemental Indenture and shall in no way
modify or restrict any of the terms or provisions hereof.

                                      - 4 -

<PAGE>   6

         SECTION 3.09 Counterparts. This Supplemental Indenture may be executed
in counterparts, each of which shall for all purposes be deemed to be an
original, and all such counterparts shall together constitute but one and the
same instrument.

         SECTION 3.10 Notices. The addresses for notices to the Company and the
Trustee set forth in Section 11.02 of the Original Indenture shall be amended,
without further action, to read in their entirety as follows:

                  "If to the Company:

                           Tele-Communications, Inc.
                           9197 South Peoria Street
                           Englewood, Colorado 80112
                           Attention: Treasurer

                  If to the Trustee:

                           State Street Bank and Trust Company
                           Goodwin Square
                           225 Asylum Street
                           23rd Floor
                           Hartford, Connecticut 06103
                           Attention:  Corporate Trust Department"

         SECTION 3.11 Governing Law. This Supplemental Indenture shall be
governed by and construed in accordance with the internal laws of the State of
New York.

                                      - 5 -

<PAGE>   7

         IN WITNESS WHEREOF, the parties hereto have caused this Supplemental
Indenture to be duly executed as of the day and year first above written.

                                     TELE-COMMUNICATIONS, INC.

                                     By:
                                        ---------------------------------------
                                        Name:
                                        Title:

                                     STATE STREET BANK AND TRUST COMPANY,
                                               as Trustee

                                     By:
                                        ---------------------------------------
                                        Name:
                                        Title:

                                      - 6 -

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