Document:

<PAGE>

                                  EXHIBIT 10.48

                            Liberty Media Corporation

                                December 7, 2000

UnitedGlobalCom. Inc.
4643 South Ulster Street
Denver, Colorado 80237

Gentlemen:

     This letter confirms the terms and conditions of our agreement and
understanding regarding the transactions (the "TRANSACTIONS") described herein
and in the Summary of Terms attached hereto (the "SUMMARY" and together
herewith, this "AGREEMENT"). Capitalized terms not otherwise defined herein
shall have the meanings ascribed to them in the Summary.

     As an inducement to LMC to enter into and perform its obligations under
this Agreement, UGC hereby represents and warrants to LMC as follows:

     (a)  UGC has all requisite power and authority to execute and deliver
and perform its obligations under this Agreement and each document or
agreement to be executed and delivered by it pursuant to this Agreement
(collectively, with this Agreement, the "TRANSACTION DOCUMENTS"), and to
consummate the Transactions. The execution and delivery by UGC of this
Agreement and the other Transaction Documents, the consummation of the
Transactions and the performance by it of its obligations hereunder and
thereunder have been duly authorized by the Board of Directors of UGC and all
other requisite corporate action. This Agreement has been, and each of the
other Transaction Documents will be, duly and validly executed and delivered
by UGC. Assuming the due execution and delivery by LMC, this Agreement
constitutes, and each of the other Transaction Documents when executed and
delivered by UGC will constitute, the legal, valid and binding obligation of
UGC, enforceable in accordance with its terms, except as such enforceability
may be affected by applicable bankruptcy, reorganization, insolvency,
moratorium or similar laws affecting creditors' rights generally or by
general equitable principles.

     (b)  No consent, approval or waiver of, notice to, or filing with, any
other individual, corporation, limited liability company, partnership, joint
venture, Governmental Authority (as defined below), business association or
other entity ("PERSON") is required on behalf of UGC or any of its subsidiaries
in connection with the execution, delivery or performance by UGC of this
Agreement or any of the other Transaction Documents, or the consummation of the
Transactions (including, without limitation, the commitment to make and the
making of the UGC Loan and, if applicable, the acquisition of UPC Shares in
payment of the UGC Loan). The execution and delivery of this Agreement and the
other Transaction Documents by UGC do not, and the performance by UGC of its
obligations hereunder and thereunder (including, without limitation, the
commitment to make and the making of the UGC Loan and, if applicable, the
acquisition of UPC Shares in payment of the UGC Loan), will not, (i) violate or
conflict with any provision of the

<PAGE>

UnitedGlobalCom, Inc.
December 7, 2000
Page 2

certificate of incorporation, bylaws, operating agreement or other
organizational or governing documents of UGC or any of its subsidiaries, (ii)
violate any of the terms, conditions or provisions of any federal, state,
local or foreign law (common or civil), statute, code, ordinance, decree,
rule or regulation ("LAW"), or any order, writ, injunction, award, judgment,
ruling or decree ("JUDGMENT") of any federal, state, local or foreign court
or governmental or regulatory agency, authority, commission or
instrumentality ("GOVERNMENTAL AUTHORITY") to which any of UGC or any of its
subsidiaries is subject or by which any of the foregoing or any of their
respective assets are bound, or (iii) result in a violation or breach of, or
constitute (with or without due notice or lapse of time or both) a default
(or give rise to any right of termination, cancellation or acceleration)
under, or result in any mortgage, pledge, lien, encumbrance, charge or
security interest ("LIEN") on any of the assets of UGC or any of its
subsidiaries pursuant to, any note, bond, indenture, debenture, security
agreement, trust agreement, lien, mortgage, lease, agreement, contract,
license, franchise, permit, guaranty, joint venture agreement, or other
agreement, instrument, understanding, commitment or obligation, oral or
written (collectively "CONTRACTS"), to which UGC or any of its subsidiaries
is a party or by which UGC or any of its subsidiaries or any of their
respective assets is bound, except, in the case of clauses (ii) and (iii), as
would not, individually or in the aggregate, adversely affect (x) the ability
of UGC to perform its obligations under this Agreement or (y) the business,
assets, financial or other condition, results of operations or prospects of
UGC or any of its subsidiaries.

     (c)  UPC is a foreign issuer (within the meaning of the Hart-Scott-Rodino
Antitrust Improvements Act of 1976, as amended ( the "HSR ACT")) and that it,
together with all entities that it controls (within the meaning of the HSR Act),
(i) does not hold assets located in the United States having an aggregate book
value of $15 million or more and (ii) did not make aggregate sales in or into
the United States of $25 million or more in its most recently concluded fiscal
year.

     As an inducement to UGC to enter into and perform its obligations under
this Agreement, LMC hereby represents and warrants to UGC as follows:

     (1)  LMC has all requisite power and authority to execute and deliver
and perform its obligations under this Agreement and each Transaction
Document to be executed and delivered by it pursuant to this Agreement and to
consummate the Transactions. The execution and delivery by LMC of this
Agreement and the other Transaction Documents, the consummation of the
Transactions and the performance by it of its obligations hereunder and
thereunder have been duly authorized by the Board of Directors of LMC and all
other requisite corporate action. This Agreement has been, and each of the
other Transaction Documents will be, duly and validly executed and delivered
by LMC. Assuming the due execution and delivery by UGC, this Agreement
constitutes, and each of the other Transaction Documents when executed and
delivered by LMC will constitute, the legal, valid and binding obligation of
LMC, enforceable in accordance with its terms, except as such enforceability
may be affected by applicable bankruptcy, reorganization, insolvency,
moratorium or similar laws affecting creditors' rights generally or by
general equitable principles.

<PAGE>

UnitedGlobalCom, Inc.
December 7, 2000
Page 3

     (2)  No consent, approval or waiver of, notice to, or filing with, any
other Person is required on behalf of LMC or any of its subsidiaries in
connection with the execution, delivery or performance by LMC of this
Agreement or any of the other Transaction Documents, or the consummation of
the Transactions (including, without limitation, the incurrence of the debt
and guaranty obligations to UGC contemplated hereby), except that no
representation is made with respect to any foreign law. The execution and
delivery of this Agreement and the other Transaction Documents of LMC do not,
and the performances by LMC of its obligations hereunder and thereunder
(including, without limitation, the incurrence of the debt and guaranty
obligations to UGC contemplated hereby), will not, (a) violate or conflict
with any provision of the certificate of incorporation, bylaws, operating
agreement or other organizational or governing documents of LMC or any
subsidiaries, (b) violate any of the terms, conditions or provisions of any
Law or Judgment of any Governmental Authority to which LMC or any of its
subsidiaries is subject or by which any of the foregoing or any of their
respective assets are bound, except that no representation is made with
respect to any foreign Law, or (c) result in a violation or breach of, or
constitute (with or without due notice or lapse of time or both) a default
(or give rise to any right of termination, cancellation or acceleration)
under, or result in any Lien on any of the assets of LMC or any of its
subsidiaries pursuant to, any Contract to which LMC or any of its
subsidiaries is a party or by which LMC or any of its subsidiaries or any of
their respective assets is bound, except in the case of clauses (ii) and
(iii) as would not, individually or in the aggregate, adversely affect (x)
the ability of LMC to perform its obligations under this Agreement or (y) the
business, assets, financial or other condition, results of operations or
prospects of LMC or any of its subsidiaries.

     Each party hereto shall pay its own expenses (including fees and expenses
of legal counsel, or other representatives or consultants) in connection with
the Transactions (whether or not consummated).

     Each party agrees to take all such actions as may be required to consummate
the Transactions on the terms and conditions set forth in this Agreement.

     The representations and warranties made by each party to the other
herein shall survive the execution and delivery of this Agreement and
consummation of the Transactions. Each party hereto agrees to identify and
hold harmless the other party hereto from and against any and all losses,
liabilities, damages, deficiencies, costs and expenses (including, without
limitation, reasonable attorneys' fees and expenses) resulting from, based
upon, arising out of or otherwise in respect of any inaccuracy in or breach
of any representation or warranty of the indemnifying party contained in this
Agreement or any nonperformance or breach of any covenant or agreement made
by the indemnifying party in this Agreement.

<PAGE>

UnitedGlobalCom, Inc.
December 7, 2000
Page 4

     This Agreement will be governed by and construed in accordance with the
laws of the State of Colorado without reference to the conflicts of law rules of
that jurisdiction. Each of the parties (a) will submit itself to the
non-exclusive jurisdiction of any federal court located in the State of Colorado
or any Colorado state court having subject matter jurisdiction in the event any
dispute arises out of this Agreement, (b) agrees that venue will be proper as to
any proceeding brought in any such court with respect to such a dispute, (c)
will not attempt to deny or defeat such personal jurisdiction or venue by motion
or other request for leave from any such court and (d) waives any right to a
trial by jury in any proceeding brought with respect to this Agreement or the
Transactions.

     Neither party will assign its rights or delegate its obligations under this
Agreement (including, without limitation, the rights and obligations with
respect to the UGC Loan) except to a direct or indirect wholly owned subsidiary
of such party. The party making an assignment or delegation permitted by the
foregoing sentence will, however, continue to be liable hereunder to the same
extent as if such assignment or delegation had not been made.

     Following the execution and delivery of this Agreement, the parties shall
negotiate in good faith and enter into such additional documents and agreements
as may be appropriate in connection with the Transactions, but the failure of
the parties to execute and deliver such documents or agreements will not affect
the binding effect or enforceability of this Agreement.

     Please indicate your agreement with the foregoing by signing a copy of this
letter in the space provided and returning it to the undersigned.

                                        Sincerely,

                                        LIBERTY MEDIA CORPORATION

                                        By: /s/ Charles Y. Tanabe
                                            --------------------------
                                        Name:  Charles Y. Tanabe
                                        Title: Senior Vice President

Accepted and Agreed:

UNITEDGLOBALCOM, INC.

By: /s/ Ellen P. Spangler
   -----------------------
Name: Ellen P. Spangler
Title: Senior Vice President

<PAGE>

                              SUMMARY OF TERMS

Parties:            UnitedGlobalCom, Inc. ("UGC") and Liberty Media Corporation
                    ("LMC")

Definitions:        As used herein, terms with initial capital letters that are
                    not defined herein will have the meaning ascribed to them in
                    the June 25, 2000 agreement among UGC, United Pan-Europe
                    Communications N.V. ("UPC"), Liberty Media International,
                    Inc. ("LMI") and LMC (as amended to date and as it may be
                    amended in the future, and including, if applicable, the
                    definitive agreement contemplated thereby, the "June
                    Agreement").

UGC Loan:           UGC will loan LMC up to $510 million (the "UGC Loan") to
                    provide LMC with funds (i) to satisfy LMI's obligations
                    under the letter agreement dated March 27, 2000, between AMI
                    GP Ltd. (as it may be amended or restated either with UGC's
                    consent or on terms that are no less favorable in any
                    material respect to LMI than those that are in effect as of
                    the date hereof, the "Hicks Agreement") and (ii) to retire
                    debt of Cablevision S.A. that is guaranteed by LMI (each
                    purpose described in clause (i) or (ii) being referred to as
                    a "Permitted Purpose"). Interest on unpaid principal of the
                    UGC Loan will be payable at the rate of 8% per annum, and
                    all interest and principal will be due and payable in full
                    on the first to occur of (i) the date on which New United
                    shall have acquired all the Contributed Subs pursuant to the
                    June Agreement (the "June Agreement Closing Date"), (ii)
                    termination of the June Agreement and (iii) June 30, 2001.
                    The first advance of proceeds of the UGC Loan will be $200
                    million (the "First Advance") and will be made within one
                    business day after the date hereof. UGC will make one or
                    more other advances (the "Subsequent Advances") totaling up
                    to $310 million at such time or times as LMC may request for
                    one or more Permitted Purposes. LMC may request that UGC
                    make a Subsequent Advance by giving at least three business
                    days' prior notice to UGC setting forth (i)
<PAGE>

                    the amount requested, (ii) evidence reasonably satisfactory
                    to UGC that LMC or LMI or a subsidiary of LMC or LMI has
                    paid or is obligated to pay the amount requested for one or
                    more Permitted Purposes, (iii) the date the Subsequent
                    Advance is to be made and (iv) wire transfer instructions,
                    which notice must be given at least three business days
                    before the date that the advance is to be made. LMC's
                    obligation with respect to the First Advance will be
                    evidenced by a promissory note in the form attached as
                    Exhibit A (the "First Advance Note"). The obligations with
                    respect to Subsequent Advance(s) will be evidenced by a
                    promissory note in the form attached as Exhibit B
                    (the"Subsequent Advance Note"), with such modifications as
                    may be necessary (a) to provide for multiple advances of
                    loan proceeds and (b) to reflect as the obligor on the
                    Subsequent Advance Note the subsidiary of LMC or LMI that
                    acquires, pursuant to the Hicks Agreement, an interest in or
                    with respect to Cablevision S.A. to be acquired by New
                    United pursuant to the June Agreement. The obligations under
                    the Subsequent Advance Note will be unconditionally
                    guaranteed by LMC pursuant to a guaranty in the form
                    attached as Exhibit C until the earlier of (i) payment in
                    full of the Subsequent Advance Note and (ii) the closing of
                    the acquisition by New United of the subsidiary of LMC that
                    is the obligor under the Subsequent Advance Note, at which
                    time LMC will cease to have any liability on account of that
                    guaranty. The making of the UGC Loan will not relieve UGC of
                    any of its obligations under the June Agreement with respect
                    to the Hicks Agreement or the costs of acquiring the
                    interest in or with respect to Cablevision S.A. or on
                    account of debt of Cablevision S.A. as contemplated by the
                    June Agreement.

Payment of the      If the June Agreement Closing Date has not occurred by June
UGC Loan:           30, 2001, or if by that date the June Agreement shall have
                    been terminated, LMC will pay or cause to be paid all unpaid
                    principal and interest on the UGC Loan either in cash or, at
                    LMC's election, in cash and by the delivery of Series 1
                    Convertible Class

                                      -2-
<PAGE>

                    A Preference Shares ("UPC Shares") of UPC. For that purpose,
                    each UPC Share will be deemed to have a value equal to its
                    Liquidation Preference (as defined in the resolution of
                    UPC's Board of Management authorizing the UPC Shares).

Amendments to       The June Agreement will be amended to provide that, with
June Agreement:     respect to the indebtedness owed by one or more Contributed
                    Subs (or by subsidiaries of one or more Contributed Subs)
                    and evidenced by promissory notes to be retained by LMC or
                    LMI after such obligor(s) are acquired by New United, as
                    described in the penultimate paragraph of paragraph 1 of
                    Exhibit A to the June Agreement (the "Retained Debt"): (a)
                    UGC will cause the obligor(s) on the Retained Debt (i) to
                    pay the Retained Debt (other than the Retained Debt
                    described in clause (a) of the penultimate paragraph of
                    paragraph 1 of Exhibit A to the June Agreement (the
                    "18-Month Retained Debt")) in full at the time of the
                    closing of New United's acquisition of such obligor(s) and
                    (ii) to pay the 18-Month Retained Debt in accordance with
                    its terms, and (b) LMC will cause the obligor on the
                    18-Month Retained Debt to pay in full all interest accrued
                    on the 18-Month Retained Debt to the June Agreement Closing
                    Date, such payment to be made from sources other than the
                    assets (as described in the June Agreement) to be
                    transferred to New United through the transfer of ownership
                    of such obligor. In addition, the June Agreement will be
                    amended (i) to change "March 31, 2001" in the last sentence
                    of paragraph 3 of the June Agreement to "June 30, 2001" and
                    (ii) to provide that if by May 31, 2001, New United has
                    acquired some but not all of the Contributed Subs, the
                    parties will negotiate in good faith (i) a reasonable
                    extension of the June 30, 2001 date referenced in the
                    preceding clause (i) and of the maturity date of the UGC
                    Loan and (ii) the terms on which the transactions
                    contemplated by the June Agreement can be completed
                    including, for example, provisions for restructuring the
                    manner in which the transfer of assets intended to be
                    transferred to New United pursuant to the June Agreement can
                    be effected.

                                      -3-
<PAGE>

                                    EXHIBIT A
                              {FIRST ADVANCE NOTE)

                                 PROMISSORY NOTE

$200,000,000                                                   Denver, Colorado
                                                               December ___,2000

     FOR VALUE RECEIVED, the undersigned, Liberty Media Corporation (the
"Borrower"), hereby promises to pay to UNITEDGLOBALCOM, INC., a Delaware
corporation (the "Company" and together with any of its permitted successors or
assigns, the "Holder"), at 4643 South Ulster Street, Suite 1300, Denver,
Colorado 80237, or at such other place as Holder may designate in writing from
time to time, the principal sum of $200,000,000 or, if less, the unpaid
principal balance of such amount, with interest as set forth in this Note. Terms
with initial capital letters that are not defined herein have the meaning
ascribed to them in the letter agreement dated December 7, 2000, between the
Borrower and the Company ("the December Agreement"). This Note and all accrued
but unpaid interest shall be due and payable on the earliest of (1) the June
Agreement Closing Date, (ii) the termination of the June Agreement prior to the
June Agreement Closing Date and (iii) June 30, 2001. The date on which this Note
and all accrued but unpaid interest shall be due and payable is described in
this Note as the "Maturity Date."

     From the date of this Note and until this Note is paid in full, interest on
the outstanding principal amount of this Note shall accrue at a rate equal to 8%
per annum.

     If the Maturity Date is not a Business Day (as defined below), all amounts
due and payable on the Maturity Date shall be paid on the next Business Day. All
interest shall be calculated on the basis of a year consisting of 365 days and
the actual number of days elapsed until this Note is paid in full.

     All payments of principal and interest in respect of this Note (other than
pursuant to the Borrower Put or the Holder Call, as defined below) shall be made
in immediately available funds to the order of the Holder by wire transfer to an
account as may be specified from time to time by the Holder to the Borrower in
writing or, at the option of the Holder, in such manner as the Holder shall have
designated to the Borrower in writing.

     "Business Day" shall mean any day other than Saturday, Sunday or a day on
which banks are required or permitted to close in Denver, Colorado.

     In the event that the June Agreement Closing Date has not occurred by June
30, 2001, the Borrower may elect to repay all principal and accrue interest in
respect of this Note either in

                                      A-1
<PAGE>

cash or by tendering UPC Shares to the Company, or by a combination of those two
forms of payment. For purposes of this Note, each UPC Share will be deemed to
have a value equal to its Liquidation Preference (as defined in the resolution
of the Company's Board of Management authorizing the UPC Shares), determined as
of the date the UPC Share are tendered to the Company. Any payment under this
Note that is made by the tender of UPC Shares will be deemed made on the date of
delivery of certificates representing the UPC Shares, duly endorsed for transfer
or accompanied by duly executed stock assignments, or of any other instrument
that is effective to transfer ownership of UPC Shares to the Company.

     All payments under this Note shall be credited first toward interest then
accrued and the remainder toward principal. The Borrower may prepay this Note,
in whole or in part, at any time without premium or penalty. All payments of the
unpaid principal balance and interest will be made without withholding or
deduction for or on account of any present or future taxes, duties, assessments
or governmental charges of whatever nature, unless the withholding of such taxes
or duties is required by law.

     If an attorney is engaged by the Holder to enforce or construe any
provision of this Note and the Holder prevails in any related court
proceeding, the Borrower shall pay, on demand, all attorneys' fees and all
other costs incurred by the Holder, together with interest on such amount
from the date that is 10 days after such demand until paid, at the rate of
interest payable under this Note plus an additional 3 percent.

     Except as expressly provided in this Note, the Borrower and all endorsers
waive presentment, demand, and notice of dishonor.

     No delay or failure of the Holder in the exercise of any right or remedy
under this Notes shall be deemed a waiver of such right, and no exercise or
partial exercise of any right or remedy shall be deemed a waiver of any other
right or remedy that the Holder may have.

     This Note shall be governed by and construed in accordance with the laws of
the State of Colorado. The Borrower hereby submits to the jurisdiction of the
United States District Court for the District of Colorado and of any court of
the State of Colorado sitting in Denver, Colorado, for purposes of all legal
proceedings arising out of or related to this Note. The Borrower irrevocably
waives, to the fullest extend permitted by law, any objection that the Borrower
may now or later have to the lack of personal jurisdiction or laying of the
venue of any such proceeding brought in such a court and any claim that any such
proceedings brought in a court has been brought in an inconvenient forum.
Notwithstanding the preceding two sentences, the Holder retains the right to
bring any suit, action or proceeding seeking to enforce any provision of, or
based on any matter arising out of or in connection with this Note in any court
that has jurisdiction over the Borrower and subject matter.

     This Note and the rights hereunder may be assigned or transferred by the
Company only to a direct or indirect wholly owned subsidiary of the company.

                                      A-2
<PAGE>

     IN WITNESS WHEREOF, the Borrower has duly executed this Note as of the
date first written above.

                                        BORROWER:

                                        LIBERTY MEDIA CORPORATION

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

                                      A-3
<PAGE>

                                    EXHIBIT B
                            (SUBSEQUENT ADVANCE NOTE)

                                 PROMISSORY NOTE

$310,000,000                                             Denver, Colorado
                                                         ________________, _____

     FOR VALUE RECEIVED, the undersigned, Liberty Argentina, Inc. (the
"Borrower"), hereby promises to pay to UNITEDGLOBALCOM, INC., a Delaware
corporation (the "Company" and together with any of its permitted successors
or assigns, the "Holder"), at 4643 South Ulster Street, Suite 1300, Denver,
Colorado 80237, or at such other place as Holder may designate in writing
from time to time, the principal sum of $310,000,000 or, if less, the unpaid
principal balance of such amount, with interest as set forth in this Note.
Terms with initial capital letters that are not defined herein have the
meaning ascribed to them in the letter agreement dated December 7, 2000,
between Liberty Media Corporation and the Company ("the December Agreement").
This Note and all accrued but unpaid interest shall be due and payable on the
earliest of (1) the June Agreement Closing Date, (ii) the termination of the
June Agreement prior to the June Agreement Closing Date and (iii) June 30,
2001. The date on which this Note and all accrued but unpaid interest shall
be due and payable is described in this Note as the "Maturity Date."

     The principal amount of each advance made by the Company and the amount of
each payment or prepayment made by the Borrower shall be recorded by the Company
on the schedule attached, hereto; provided that any failure to make any such
recordation shall not affect the Borrower's obligation in respect of such
advance.

     From the date of this Note and until this Note is paid in full, interest on
the outstanding principal amount of this Note shall accrue at a rate equal to 8%
per annum.

     If the Maturity Date is not a Business Day (as defined below), all amounts
due and payable on the Maturity Date shall be paid on the next Business Day. All
interest shall be calculated on the basis of a year consisting of 365 days and
the actual number of days elapsed until this Note is paid in full.

     All payments of principal and interest in respect of this Note (other than
pursuant to the Borrower Put or the Holder Call, as defined below) shall be made
in immediately available funds to the order of the Holder by wire transfer to an
account as may be specified from time to time by the Holder to the Borrower in
writing or, at the option of the Holder, in such manner as the Holder shall have
designated to the Borrower in writing.

                                      B-1
<PAGE>

     "Business Day" shall mean any day other than Saturday, Sunday or a day on
which banks are required or permitted to close in Denver, Colorado.

     In the event that the June Agreement Closing Date has not occurred by
June 30, 2001, the Borrower may elect to repay all principal and accrued
interest in respect of this Note either in cash or by tendering UPC Shares to
the Company, or by a combination of those two forms of payment. For purposes
of this Note, each UPC Share will be deemed to have a value equal to its
Liquidation Preference (as defined in the resolution of the Company's Board
of Management authorizing the UPC Shares), determined as of the date the UPC
Shares are tendered to the Company. Any payment under this Note that is made
by the tender of UPC Shares will be deemed made on the date of delivery of
certificates representing the UPC Shares, duly endorsed for transfer or
accompanied by duly executed stock assignments, or of any other instrument
that is effective to transfer ownership of UPC Shares to the Company.

     All payments under this Note shall be credited first toward interest then
accrued and the remainder toward principal. The Borrower may prepay this Note,
in whole or in part, at any time without premium or penalty. All payments of the
unpaid principal balance and interest will be made without withholding or
deduction for or on account of any present or future taxes, duties, assessments
or governmental charges of whatever nature, unless the withholding of such taxes
or duties is required by law.

     If an attorney is engaged by the Holder to enforce or construe any
provision of this Note and the Holder prevails in any related court
proceeding, the Borrower shall pay, on demand, all attorneys' fees and all
other costs incurred by the Holder, together with interest on such amount
from the date that is 10 days after such demand until paid, at the rate of
interest payable under this Note plus an additional 3 percent.

     Except as expressly provided in this Note, the Borrower and all endorsers
waive presentment, demand, and notice of dishonor.

     No delay or failure of the Holder in the exercise of any right or remedy
under this Notes shall be deemed a waiver of such right, and no exercise or
partial exercise of any right or remedy shall be deemed a waiver of any other
right or remedy that the Holder may have.

     This Note shall be governed by and construed in accordance with the laws of
the State of Colorado. The Borrower hereby submits to the jurisdiction of the
United States District Court for the District of Colorado and of any court of
the State of Colorado sitting in Denver, Colorado, for purposes of all legal
proceedings arising out of or related to this Note. The Borrower irrevocably
waives, to the fullest extent permitted by law, any objection that the Borrower
may now or later have to the lack of personal jurisdiction or laying of the
venue of any such proceeding brought in such a court and any claim that any such
proceedings brought in a court has been brought in an inconvenient forum.
Notwithstanding the preceding two sentences, the Holder retains the right to
bring any suit, action or proceeding seeking to enforce any provision of, or
based on any matter arising out of or in connection with this Note in any court
that has jurisdiction over the Borrower and subject matter.

                                      B-2
<PAGE>

     This Note and the rights hereunder may be assigned or transferred by the
Company only to a direct or indirect wholly owned subsidiary of the Company.

     IN WITNESS WHEREOF, the Borrower has duly executed this Note as of the dare
first written above.

                                        BORROWER:

                                        LIBERTY ARGENTINA, INC.

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

                                      B-3
<PAGE>

                           SCHEDULE TO PROMISSORY NOTE

                         LOANS AND PAYMENTS OF PRINCIPAL

<TABLE>
<CAPTION>
                                        AMOUNT OF
                                        PRINCIPAL                UNPAID
                    AMOUNT              PAYMENT OR               PRINCIPAL           NOTATION
  DATE              OF LOAN             PREPAYMENT               BALANCE             MADE BY
  ----              -------             ----------               -------             --------
<S>                 <C>                 <C>                      <C>                 <C>

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</TABLE>

                                      B-4
<PAGE>

                                    EXHIBIT C

UnitedGlobalCom, Inc.
4643 South Ulster Street
Suite 1300
Denver, Colorado 80237

Dear Sir or Madam:

     For and in consideration of UnitedGlobalCom, Inc.'s extending credit to
Liberty Argentina, Inc. (the "Borrower"), at Liberty Media Corporation's request
(as evidenced by its execution hereof), the undersigned, Liberty Media
Corporation (the "Guarantor"), for itself, its successors and assigns, hereby
unconditionally guarantees to UnitedGlobalCom, Inc. (the "Lender"), its
successors and assigns, the payment of any indebtedness of the Borrower to the
Lender under the promissory note dated ____________, _____ in the principal
amount of up to $310,000,000, a copy of which is attached hereto (the "Note"),
together with all interest, and charges thereon (this "Guaranty"). Upon failure
by the Borrower to pay punctually any guaranteed amount, the Guarantor shall
forthwith on demand pay the amount not so paid at the place and in the manner
specified in the Note.

     This Guaranty is executed and delivered pursuant to a letter agreement
dated December 7, 2000, between the Lender and the Guarantor (the "December
Agreement"). Terms with initial capital letters that are not defined in this
Guaranty will have the meaning ascribed to them in the December Agreement.

     The obligation of the Guarantor hereunder is separate and independent from
the obligation of the Borrower, and such obligation shall not be released,
discharged or otherwise affected by:

          (i)  any extension, renewal, settlement, compromise, waiver or
     release in respect of any obligation of the Borrower under the Note, by
     operation of law or otherwise;

          (ii) any modification or amendment of or supplement to the Note;

          (iii) any release, impairment, non-perfection or invalidity of any
     direct or indirect security for any obligation of the Borrower under the
     Note;

          (iv) any change in the corporate existence, structure or ownership of
     the Borrower, or any insolvency, bankruptcy, reorganization or other
     similar proceeding affecting the

                                      C-1
<PAGE>

UnitedGlobalCom, Inc.
______________, 2000
Page 2

     Borrower or its assets or any resulting release or discharge of any
     obligation of the Borrower contained in the Note; or

          (v)  any act or omission to act or delay of any kind by the Lender
     which might, but for the provisions of this paragraph, constitute a legal
     or equitable discharge of the Borrower's obligations under the Note.

     The Guarantor's obligations hereunder shall remain in full force and effect
until the earlier of (a) the time that all amounts owed by the Borrower under
the Note have been paid an full and (b) the closing of the acquisition of the
Borrower by the Lender or New United as contemplated by the December Agreement.
If at any time any amount payable by the Borrower under the Note is rescinded or
must be otherwise restored or returned upon the insolvency, bankruptcy or
reorganization of the Borrower or otherwise, the Guarantor's obligations
hereunder with respect to such payment shall be reinstated at such time as
though such payment had been due but not made at such time, except that the
Guarantor's obligations shall not be subject to such reinstatement after the
event described in clause (b) of the foregoing sentence.

     The Guarantor waives promptness, diligence, notice of acceptance,
presentment, demand, protest and notice of dishonor with respect to any
obligation of this Guaranty and any requirement that the Lender exhaust any
right or take any action against the Borrower or any collateral security.

     The Guarantor shall be subrogated to all rights of the Lender against the
Borrower in respect of any amounts paid by the Guarantor pursuant to this
Guaranty; provided, however, that the Guarantor shall not, without the consent
of the Lender, be entitled to enforce or to receive any payments arising out of
or based upon such right of subrogation until all amounts owed to the Lender
under the Note have been paid in full.

     All rights, obligations, and liabilities arising under this Guaranty shall
be construed in accordance with the laws of the State of Colorado.

     IN WITNESS WHEREOF, this Guaranty has been duly executed and delivered on
the day and year first written above.

                                     LIBERTY MEDIA CORPORATION

                                     By:
                                        --------------------------------
                                        Charles Y. Tanabe, Senior Vice President

                                      C-2<PAGE>

                                  EXHIBIT 10.51

                              CONSULTING AGREEMENT

     This Consulting Agreement ("Agreement") is made and entered into as of the
1st day of October, 2000, by and between Tina M. Wildes whose address is 5421
South Dayton Court, Englewood, Colorado, 80111 ("Consultant") and
UnitedGlobalCom, Inc., a Delaware corporation, 4643 South Ulster Street, Suite
1300, Denver, Colorado 80237 ("United").

     WHEREAS, Consultant has resigned as Senior Vice President, Development
Oversight and Administration, of United and has agreed to serve as a Consultant
to United on the terms of this Agreement; and

     WHEREAS, Consultant has significant experience in telecommunications
operations and United intends to call upon that experience as it considers
advisable in its absolute discretion in connection with its telecommunications
business;

     THEREFORE, in consideration of the mutual covenants hereinafter set forth,
Consultant and United agree as follows:

1.   ENGAGEMENT OF CONSULTANT

     United hereby engages Consultant as a consultant, and Consultant accepts
     such engagement, pursuant to the provisions of this Agreement. Consultant
     acknowledges and agrees that, for all purposes, Consultant shall be an
     independent contractor and not an employee of United.

2.   CONSULTING PERIOD

     Consultant shall be available to consult with United on reasonable notice
     during the period from October 1, 2000 to October 1, 2001 (the "Consulting
     Period").

3.   CONSIDERATION

     a.   During the Consulting Period, United shall pay to Consultant a fee of
          $15,000 per calendar month (the "Consulting Fee"). In addition, during
          the Consulting Period, the stock options granted to the Consultant
          under the Stock Option Plans for United, United Pan-Europe
          Communications N.V., chello broadband N.V., United Latin America,
          Inc., and Austar United Communications Limited shall continue to vest
          in the same monthly amounts in accordance with such Plans. Vesting on
          all options will terminate as of October 1, 2001. All vested options
          will be exercisable pursuant to the provisions of the respective
          Plans.

          Notwithstanding the foregoing, in the event Consultant does not
          exercise any or all of the incentive stock option grants Consultant
          received while an

<PAGE>

          employee of United within 90 days of September 30, 2000, such grants
          will thereafter be treated as non-qualified options for tax purposes.
          Consultant hereby acknowledges that her failure to exercise incentive
          stock options within such time period will cause all such unexercised
          incentive stock options to be treated as non-qualified options for tax
          purposes.

     b.   In addition to the Consulting fee, United agrees to pay for the
          monthly premium amount incurred for a $360,000 whole life policy on
          Consultant for the period of October 1, 2000 to January 31, 2001. In
          the event Consultant is unable to obtain life insurance through her
          spouse's employer, because of a pre-existing condition directly caused
          by complications from giving birth to a child, United agrees to
          continue to pay the monthly premium amount for such insurance until
          March 31, 2001.

     c.   United agrees to reimburse Consultant for normal business expenses
          incurred in the performance of this Agreement, including the
          following, provided that any single expense in excess of $200 must
          receive prior written approval from United:

          (i)  Air travel (coach class on domestic flights and business class on
               international flights) to and from Denver, provided all travel
               receives the prior written approval of United; and

          (ii) Hotel, taxis and other reasonable travel expenses incurred while
               conducting business for United. The reasonableness of any expense
               shall be determined by United in its sole discretion.

          All reimbursement of the above expenses will be consistent with
          United's Business Expense Policy, as such policy may be amended from
          time to time ("Expense Policy").

     d.   The Consulting Fee shall be paid on the 1st day of each calendar month
          during the Consulting Period. All business expenses will be paid
          within thirty (30) days after submission by Consultant to United of a
          completed expense report with receipts as required pursuant to the
          Expense Policy.

4.   RETURN OF PROPERTY

     Upon the termination of this Agreement, Consultant will return to United
     all property of United or any of its affiliates including, without
     limitation, all copies of any documents or other records in Consultant's
     possession or control that contain Confidential Information, as well as
     parking and building passes, keys, credit cards, fax, computer, cell phone,
     any other business-related property or equipment that was purchased for
     Consultant or provided to Consultant for use in performing her duties under
     this Agreement.

                                       2
<PAGE>

5.   CONFIDENTIALITY

     Consultant acknowledges and agrees that any information or documentation
     concerning United or any of its affiliates that Consultant develops or is
     provided during the term of this Agreement or any extensions thereof
     (including, without limitation, data, agreements, business plans or
     proposals) is confidential and proprietary to United (the "Confidential
     Information"). Consultant therefore agrees not to disclose any Confidential
     Information to anyone outside of United or its affiliates. Likewise,
     Consultant agrees never to use any Confidential Information for any
     personal purpose or advantage, but only in the performance of Consultant's
     duties hereunder. If United publicly discloses any particular information
     or documentation that was Confidential Information, then that particular
     information or documentation shall cease to be Confidential Information
     within the meaning of this Agreement. Consultant agrees that following the
     termination of this Agreement, whether by Consultant or by United,
     Consultant shall continue to be bound to comply with the provisions of this
     paragraph.

6.   NON-COMPETITION

     During the term of this Agreement, Consultant will not individually, with
     third parties or on behalf of third parties, investigate or develop
     business opportunities with respect to, or enter into negotiations,
     agreements, consulting contracts or partnerships with any company or
     individual for the purpose of pursuing multi-channel television, related
     media or other telecommunications business opportunities in any market for
     which Consultant performed any work pursuant to this Agreement. Consultant
     agrees that the provisions of this paragraph are reasonably intended to
     protect Confidential Information of United to which Consultant becomes
     privy during the Term of this Agreement.

7.   MISCELLANEOUS

     a.   LAWS, RULES AND REGULATIONS. Consultant agrees that she will not
          contravene any laws of any country or violate any regulations or
          established rules of conduct in the performance of her duties on
          behalf of United, including, but not limited to, any action that could
          constitute a violation of the U.S. Foreign Corrupt Practices Act. In
          addition, Consultant has received a copy of United's Statement of
          Policies and Procedures for Compliance with the Foreign Corrupt
          Practices Act and Standards for Ethical Business Conduct and agrees to
          comply with the provisions thereof.

     b.   INDEMNITY. Consultant further agrees to indemnify and hold harmless
          United for and from any loss or expense (including reasonable
          attorney's fees) arising out of any action or omission by Consultant
          or any other

                                       3
<PAGE>

          individual or corporation used by Consultant in the performance of her
          duties hereunder.

     c.   NOTICE. Any notice given under this Agreement shall be in writing,
          shall be sent by facsimile or by hand or messenger delivery, or by
          Federal Express or similar overnight delivery service to the other
          party at the address below, unless either party at any time or times
          designates another address for itself by notifying the other party
          thereof, in which case all notices to such party thereafter be given
          at its most recently so designated address.

          To Consultant:      Tina M. Wildes
                              5421 South Dayton Court
                              Englewood, Colorado  80111
                              Facsimile: 303-796-7109

          To United:          UnitedGlobalCom, Inc.
                              4643 South Ulster Street, Suite 1300
                              Denver, Colorado  80237
                              Facsimile: 303-770-4207
                              Attention: Chairman
                              Copy to: Legal Department

     d.   ENTIRE AGREEMENT; AMENDMENTS. This Agreement contains the entire
          understanding of the parties and supersedes any and all prior
          understandings of the parties hereto relating to the subject matter
          herein. This Agreement may not be modified except in writing executed
          by both parties hereto.

     e.   ASSIGNABILITY. No party may assign its rights and/or obligations under
          this Agreement without the written consent of the other party.

     f.   HEADINGS. The titles and headings of the sections in this Agreement
          are for convenience only and shall not in any way affect the
          interpretation of this Agreement.

     g.   GOVERNING LAW. This Agreement shall be governed by the laws of the
          State of Colorado.

                                       4
<PAGE>

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

UnitedGlobalCom, Inc.

By: /s/ Ellen P. Spangler                              November 1, 2000
   ----------------------------                        ---------------------
                                                       Date
   Its: Senior Vice President
       ------------------------

/s/ Tina M. Wildes                                     October 15, 2000
-------------------------------                        ---------------------
Tina M. Wildes                                         Date

                                       5

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