Document:

<PAGE>   1
                                                                     EXHIBIT 4.5

                              DECLARATION GUARANTEE

         DECLARATION GUARANTEE (this "Agreement"), dated as of March 21, 2000,
among the undersigned trustees (the "Trustees") of TCI Communications Financing
I, a Delaware statutory business trust (the "Trust"), AT&T Broadband, LLC, a
Delaware limited liability company, as successor sponsor of the Trust (the
"Sponsor"), and AT&T Corp., a New York corporation (the "Guarantor").

         WHEREAS TCI Communications, Inc. ("TCIC"), as sponsor, and certain
trustees of the Trust entered into a Declaration of Trust, dated as of November
21, 1995, in order to establish the Trust under the Business Trust Act of the
State of Delaware (12 Del. Code Section 3801 et seq.);

         WHEREAS TCIC, as sponsor, and certain trustees of the Trust entered
into an Amended and Restated Declaration of Trust, dated as of January 29, 1996
(the "Declaration"), pursuant to which the Trust issued $500,000,000 aggregate
liquidation amount of its 8.72% Trust Originated Preferred Securities (the
"Preferred Securities") representing undivided beneficial interests in the
assets of the Trust;

         WHEREAS, as of the date hereof, the Sponsor is the sponsor of the Trust
and the Trustees constitute all of the trustees of the Trust; and

         WHEREAS the Guarantor desires to irrevocably and unconditionally
guarantee, on a subordinated basis, the full and punctual payment (within
applicable grace periods) of all the obligations of the Sponsor under the
Declaration.

         NOW THEREFORE, in consideration of the mutual promises contained herein
and for other good and valuable consideration, the receipt and sufficiency of
which is hereby acknowledged, the Sponsor, the Guarantor and the Trustees hereby
agree as follows:

         SECTION 1. Definitions.

         Capitalized terms used herein but not defined herein have the meanings
ascribed to such terms in the Declaration.

         SECTION 2. The Guarantee.

         (a) The Guarantor irrevocably and unconditionally guarantees on a
subordinated basis as set forth herein (the "Guarantee"), to the Trustees and to
each Creditor and their successors and assigns, the full and punctual payment
(within applicable grace periods) of all the obligations of the Sponsor under
the Declaration.

         (b) The Guarantor further agrees that the Guarantee constitutes a
guarantee of payment and not of collection.

                                       1
<PAGE>   2

         (c) The Guarantor's obligation to make any payment hereunder may be
satisfied by causing the Sponsor to make such payment.

         (d) The Guarantor also agrees to pay any and all fees and expenses
(including reasonable counsel fees and expenses) incurred by the Trustees in
enforcing any of their respective rights under the Guarantee and the costs and
expenses of the Creditors in enforcing any of their respective rights under the
Guarantee, to the extent such costs and expenses become costs and expenses of
the Trust.

         SECTION 3. Subordination.

         The Guarantee constitutes an unsecured obligation of the Guarantor that
ranks (a) pari passu with the most senior preferred or preference stock of the
Guarantor outstanding on the date of this Agreement or hereafter issued and with
any guarantee now or hereafter entered into by the Guarantor in respect of any
preferred or preference stock of any Affiliate of the Guarantor, (b) pari passu
with the guarantees of Guarantor with respect to the obligations of the Sponsor
with respect to TCI Communications Financing II ("Trust II") and TCI
Communications Financing IV ("Trust IV") and the preferred securities issued by
Trust II and Trust IV, (c) senior in right of payment to any class or series of
common stock of the Guarantor or preferred or preference stock of the Guarantor
ranking subordinate and junior in right of payment to the most senior preferred
or preference stock of the Guarantor, each as may be outstanding on the date of
this Agreement or hereafter issued, and (d) subordinate and junior in right of
payment to all other indebtedness, obligations and liabilities of the Guarantor.

         SECTION 4. Notices.

         All notices provided for herein shall be in writing, duly signed by the
party giving such notice, and shall be delivered, telecopied or mailed by first
class mail as follows:

                  (a) if given to the Guarantor, to the Guarantor's mailing
address set forth below or such other address as the Guarantor may give notice
of to the Trust:

                           AT&T Corp.
                           32 Avenue of the Americas
                           New York, New York 10013-2412
                              Attn: Legal Department; and

                  (b) if given to the Sponsor or the Trustees, to the address
set forth in the Declaration or to such other address as such party may give
notice of to the Guarantor.

         All such notices shall be deemed to have been given when received in
person, telecopied with receipt confirmed, or mailed by first class mail,
postage prepaid except that if a notice or other document is refused delivery or
cannot be delivered because of a changed address of which no notice

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was given, such notice or other document shall be deemed to have been delivered
on the date of such refusal or inability to deliver.

         SECTION 5. Counterparts.

         This Agreement may be executed in two or more counterparts, each of
which shall constitute an original, but all of which when taken together shall
constitute but one instrument.

         SECTION 6. Headings.

         The headings of this Agreement are for reference only and shall not
limit or otherwise affect the meaning hereof.

         SECTION 7. Trustees Not Responsible for Recitals.

         The recitals herein contained are made by the Sponsor and the
Guarantor, and not by the Trustees, and the Trustees assume no responsibility
for the correctness thereof. The Trustees make no representation as to the
validity or sufficiency of this Agreement.

         SECTION 8. Separability.

         In case any one or more of the provisions contained in this Agreement
shall for any reason be held to be invalid, illegal or unenforceable in any
respect, such invalidity, illegality or unenforceability shall not affect any
other provisions of this Agreement, but this Agreement shall be construed as if
such invalid or illegal or unenforceable provision had never been contained
herein.

         SECTION 9. No Recourse Against Certain Persons.

         No past, present or future director, officer, employee or stockholder,
as such, of the Guarantor or any successor thereof shall have any liability for
any obligations of the Guarantor under this Agreement or for any claim based on,
in respect of, or by reason of, such obligations or their creation and all such
liability is hereby waived and released. Such waiver and release are part of the
consideration for the issue of this Agreement.

         SECTION 10. Amendments.

         Except with respect to any changes that, in the opinion of the board of
directors of the Guarantor, do not adversely affect the rights of Holders (in
which case no consent of Holders will be required), this Agreement may only be
amended with the prior approval of the Holders of at least a Majority in
liquidation amount of the Securities. The provisions of Section 12.2 of the
Declaration of the Trust with respect to meetings of Holders of the Securities
apply to the giving of such approval.

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         SECTION 11. GOVERNING LAW.

         THIS AGREEMENT SHALL BE GOVERNED AND CONSTRUED IN ACCORDANCE WITH THE
INTERNAL LAWS OF THE STATE OF NEW YORK.

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

                                    AT&T BROADBAND, LLC, Sponsor

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

                                    ------------------------
                                    Edward M. Dwyer, Regular Trustee

                                    ------------------------
                                    Michael P. Huseby, Regular Trustee

                                    ------------------------
                                    Mary S. Willis, Regular Trustee

                                    AT&T CORP., as Guarantor

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

                                    THE BANK OF NEW YORK, as Property Trustee

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

                                    THE BANK OF NEW YORK (DELAWARE),
                                              as Delaware Trustee

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

                                       5<PAGE>   1
                                                                     EXHIBIT 4.6

                              DECLARATION GUARANTEE

         DECLARATION GUARANTEE (this "Agreement"), dated as of March 21, 2000,
among the undersigned trustees (the "Trustees") of TCI Communications Financing
IV, a Delaware statutory business trust (the "Trust"), AT&T Broadband, LLC, a
Delaware limited liability company, as successor sponsor of the Trust (the
"Sponsor"), and AT&T Corp., a New York corporation (the "Guarantor").

         WHEREAS TCI Communications, Inc. ("TCIC"), as sponsor, and certain
trustees of the Trust entered into a Declaration of Trust, dated as of November
21, 1995, in order to establish the Trust under the Business Trust Act of the
State of Delaware (12 Del. Code Section 3801 et seq.);

         WHEREAS TCIC, as sponsor, and certain trustees of the Trust entered
into an Amended and Restated Declaration of Trust, dated as of March 24, 1997
(the "Declaration"), pursuant to which the Trust issued $200,000,000 aggregate
liquidation amount of its 9.72% Trust Preferred Securities (the "Preferred
Securities") representing undivided beneficial interests in the assets of the
Trust;

         WHEREAS, as of the date hereof, the Sponsor is the sponsor of the Trust
and the Trustees constitute all of the trustees of the Trust; and

         WHEREAS the Guarantor desires to irrevocably and unconditionally
guarantee, on a subordinated basis, the full and punctual payment (within
applicable grace periods) of all the obligations of the Sponsor under the
Declaration.

         NOW THEREFORE, in consideration of the mutual promises contained herein
and for other good and valuable consideration, the receipt and sufficiency of
which is hereby acknowledged, the Sponsor, the Guarantor and the Trustees hereby
agree as follows:

         SECTION 1. Definitions.

         Capitalized terms used herein but not defined herein have the meanings
ascribed to such terms in the Declaration.

         SECTION 2. The Guarantee.

         (a) The Guarantor irrevocably and unconditionally guarantees on a
subordinated basis as set forth herein (the "Guarantee"), to the Trustees and to
each Creditor and their successors and assigns, the full and punctual payment
(within applicable grace periods) of all the obligations of the Sponsor under
the Declaration.

         (b) The Guarantor further agrees that the Guarantee constitutes a
guarantee of payment and not of collection.

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         (c) The Guarantor's obligation to make any payment hereunder may be
satisfied by causing the Sponsor to make such payment.

         (d) The Guarantor also agrees to pay any and all fees and expenses
(including reasonable counsel fees and expenses) incurred by the Trustees in
enforcing any of their respective rights under the Guarantee and the costs and
expenses of the Creditors in enforcing any of their respective rights under the
Guarantee, to the extent such costs and expenses become costs and expenses of
the Trust.

         SECTION 3. Subordination.

         The Guarantee constitutes an unsecured obligation of the Guarantor that
ranks (a) pari passu with the most senior preferred or preference stock of the
Guarantor outstanding on the date of this Agreement or hereafter issued and with
any guarantee now or hereafter entered into by the Guarantor in respect of any
preferred or preference stock of any Affiliate of the Guarantor, (b) pari passu
with the guarantees of Guarantor with respect to the obligations of the Sponsor
with respect to TCI Communications Financing I ("Trust I") and TCI
Communications Financing II ("Trust II") and the preferred securities issued by
Trust I and Trust II, (c) senior in right of payment to any class or series of
common stock of the Guarantor or preferred or preference stock of the Guarantor
ranking subordinate and junior in right of payment to the most senior preferred
or preference stock of the Guarantor, each as may be outstanding on the date of
this Agreement or hereafter issued, and (d) subordinate and junior in right of
payment to all other indebtedness, obligations and liabilities of the Guarantor.

         SECTION 4. Notices.

         All notices provided for herein shall be in writing, duly signed by the
party giving such notice, and shall be delivered, telecopied or mailed by first
class mail as follows:

                  (a) if given to the Guarantor, to the Guarantor's mailing
address set forth below or such other address as the Guarantor may give notice
of to the Trust:

                           AT&T Corp.
                           32 Avenue of the Americas
                           New York, New York 10013-2412
                                   Attn: Legal Department; and

                  (b) if given to the Sponsor or the Trustees, to the address
set forth in the Declaration or to such other address as such party may give
notice of to the Guarantor.

         All such notices shall be deemed to have been given when received in
person, telecopied with receipt confirmed, or mailed by first class mail,
postage prepaid except that if a notice or other document is refused delivery or
cannot be delivered because of a changed address of which no notice

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was given, such notice or other document shall be deemed to have been delivered
on the date of such refusal or inability to deliver.

         SECTION 5. Counterparts.

         This Agreement may be executed in two or more counterparts, each of
which shall constitute an original, but all of which when taken together shall
constitute but one instrument.

         SECTION 6. Headings.

         The headings of this Agreement are for reference only and shall not
limit or otherwise affect the meaning hereof.

         SECTION 7. Trustees Not Responsible for Recitals.

         The recitals herein contained are made by the Sponsor and the
Guarantor, and not by the Trustees, and the Trustees assume no responsibility
for the correctness thereof. The Trustees make no representation as to the
validity or sufficiency of this Agreement.

         SECTION 8. Separability.

         In case any one or more of the provisions contained in this Agreement
shall for any reason be held to be invalid, illegal or unenforceable in any
respect, such invalidity, illegality or unenforceability shall not affect any
other provisions of this Agreement, but this Agreement shall be construed as if
such invalid or illegal or unenforceable provision had never been contained
herein.

         SECTION 9. No Recourse Against Certain Persons.

         No past, present or future director, officer, employee or stockholder,
as such, of the Guarantor or any successor thereof shall have any liability for
any obligations of the Guarantor under this Agreement or for any claim based on,
in respect of, or by reason of, such obligations or their creation and all such
liability is hereby waived and released. Such waiver and release are part of the
consideration for the issue of this Agreement.

         SECTION 10. Amendments.

         Except with respect to any changes that, in the opinion of the board of
directors of the Guarantor, do not adversely affect the rights of Holders (in
which case no consent of Holders will be required), this Agreement may only be
amended with the prior approval of the Holders of at least a Majority in
liquidation amount of the Securities. The provisions of Section 12.2 of the
Declaration of the Trust with respect to meetings of Holders of the Securities
apply to the giving of such approval.

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         SECTION 11. GOVERNING LAW.

         THIS AGREEMENT SHALL BE GOVERNED AND CONSTRUED IN ACCORDANCE WITH THE
INTERNAL LAWS OF THE STATE OF NEW YORK.

                                       4
<PAGE>   5

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

                               AT&T BROADBAND, LLC, Sponsor

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

                               ------------------------
                               Edward M. Dwyer, Regular Trustee

                               ------------------------
                               Michael P. Huseby, Regular Trustee

                               ------------------------
                               Mary S. Willis, Regular Trustee

                               AT&T CORP., as Guarantor

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

                               THE BANK OF NEW YORK, as Property Trustee

                               By:_____________________
                               Name:
                               Title:

                               THE BANK OF NEW YORK (DELAWARE),
                                         as Delaware Trustee

                               By:_____________________
                               Name:
                               Title:

                                       5

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