<PAGE>
                                                                    EXHIBIT 10.1

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                              UNITEDGLOBALCOM, INC.

                                 $1,375,000,000

                 10 3/4% SENIOR SECURED DISCOUNT NOTES DUE 2008



                          FIRST SUPPLEMENTAL INDENTURE

                          Dated as of January 24, 2002



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

                               FIRSTAR BANK, N.A.

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

                                     Trustee





           Supplementing the Indenture, dated as of February 5, 1998,
                                     between
 UnitedGlobalCom, Inc. (previously named "United International Holdings, Inc.")
                                       and
     Firstar Bank, N.A. (previously named "Firstar Bank of Minnesota, N.A.")



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




<PAGE>


                                TABLE OF CONTENT


<Table>
<Caption>
                                                                                                               Page
<S>               <C>                                                                                          <C>
ARTICLE I DEFINITIONS.............................................................................................3

ARTICLE II AMENDMENTS; RELEASE OF COLLATERAL......................................................................3
   SECTION 2.1    Effective Time..................................................................................3
   SECTION 2.2    Deletion of Certain Definitions.................................................................3
   SECTION 2.3    Amendments to Certain Definitions...............................................................4
   SECTION 2.4    Deletion of Certain Sections....................................................................4
   SECTION 2.5    Termination of Pledge Agreements and Release of Collateral......................................5
   SECTION 2.6    Amendments to Sections 4.3 and 4.4..............................................................5
   SECTION 2.7    Amendment to Section 4.10.......................................................................5
   SECTION 2.8    Amendments to Article V.........................................................................6
   SECTION 2.9    Amendments to Sections 6.1 and 6.2..............................................................6

ARTICLE III WAIVER OF DEFAULTS AND EVENTS OF DEFAULT..............................................................8
   SECTION 3.1    Effectiveness...................................................................................8
   SECTION 3.2    Waivers.........................................................................................9

ARTICLE IV MISCELLANEOUS PROVISIONS...............................................................................9
   SECTION 4.1    Concerning the Trustee..........................................................................9
   SECTION 4.2    Original Indenture Confirmed and Ratified.......................................................9
   SECTION 4.3    Severability....................................................................................9
   SECTION 4.4    Governing Law...................................................................................9
   SECTION 4.5    Table of Contents, Headings, etc................................................................9
   SECTION 4.6    Counterparts...................................................................................10
</Table>


                                      -i-
<PAGE>


                  This FIRST SUPPLEMENTAL INDENTURE is entered into as of
January 24, 2002 (this "Supplemental Indenture"), by and between
UnitedGlobalCom, Inc. (formerly named "United International Holdings, Inc."), a
corporation duly organized and existing under the laws of the State of Delaware
(the "Company"), and Firstar Bank, N.A. (formerly named "Firstar Bank of
Minnesota, N.A."), as Trustee, acting through its agent U.S. Bank Trust National
Association ("USBT").

                                   WITNESSETH:

                  WHEREAS, the Company and the Trustee are parties to an
Indenture dated as of February 5, 1998 (the "Original Indenture"), pursuant to
which the Company has issued $1,375 million aggregate principal amount at
maturity of its 10 3/4% Senior Secured Discount Notes due 2008; and

                  WHEREAS, the Company and Morgan Stanley & Co. Incorporated
(formerly "Morgan Stanley & Company, Inc."), as collateral agent (the
"Collateral Agent"), have entered into (i) an Amended and Restated Pledge
Agreement, dated as of November 22, 1995, as amended by a First Amendment to the
Amended and Restated Pledge Agreement, dated as of February 5, 1998, and (ii) a
Pledge Agreement, dated as of February 5, 1998 (the agreements referenced in
clauses (i) and (ii) being hereinafter referred to as the "Pledge Agreements");

                  WHEREAS, IDT United, Inc. (the "Purchaser") has commenced an
offer to purchase for cash (as amended or supplemented from time to time, the
"Offer") with respect to all of the outstanding Securities and, in connection
therewith, has solicited consents from the Holders to amendments (the
"Amendments") to certain provisions of the Original Indenture, to the
termination (the "Termination") of the Pledge Agreements and the release of the
Collateral from the Lien created by the Original Indenture, the Securities and
the Pledge Agreements, and to the waiver (the "Waiver") of certain Defaults or
Events of Default that have occurred, may have occurred or may occur under, and
compliance with certain provisions of, the Original Indenture, the Securities
and the Pledge Agreements;

                  WHEREAS, in accordance with the provisions of Section 9.2 of
the Original Indenture, as of the date hereof Holders of at least 66 2/3% in
principal amount at maturity of the outstanding Securities have provided their
written consents (including consents obtained in connection with the Offer) (the
"Required Consents") to the Amendments, to the Termination and release of the
Collateral from the Lien created by the Original Indenture, the Securities and
the Pledge Agreements, and to the Waiver;

                  WHEREAS, concurrently herewith, the Company and the Collateral
Agent are entering into the Termination of Pledge Agreements and Release of
Pledged Collateral (the "Termination Agreement") that memorializes the
termination of the Pledge Agreements and the release of the Collateral from the
Lien of the Pledge Agreements;

                  WHEREAS, the amendments to the Original Indenture effected
hereby, the termination of the Pledge Agreements memorialized by the Termination
Agreement and the release of the Collateral from the Lien created by the
Original Indenture, the Securities and the

<PAGE>

Pledge Agreements shall not become effective unless and until the Purchaser has
purchased the Securities pursuant to the Offer to which the Required Consents
relate; and

                  WHEREAS, the Waiver shall become effective upon the execution
of this Supplemental Indenture by the Company and the Trustee, acting through
USBT, but shall cease to be operative if the Securities to which the Required
Consents relate are not purchased pursuant to the Offer or, if earlier, the
Purchaser terminates the Offer without purchasing such Securities.


                                      -2-
<PAGE>

                  NOW, THEREFORE:

                  For and in consideration of the premises, the Company and the
Trustee are making and executing this Supplemental Indenture for the purpose of
effecting the Amendments set forth herein, releasing the Collateral from the
Lien of the Original Indenture and the Securities and effecting the Waiver set
forth herein. It is mutually covenanted and agreed as follows:

                                   ARTICLE I

                                  DEFINITIONS

                  Capitalized terms used but not defined in this Supplemental
Indenture shall have the respective meanings assigned to them in the Original
Indenture.

                                   ARTICLE II

                        AMENDMENTS; RELEASE OF COLLATERAL

         SECTION 2.1 Effective Time. Notwithstanding the execution of this
Supplemental Indenture on the date hereof, the amendments set forth herein and
the release of the Collateral from the Lien of the Original Indenture and the
Securities effected hereby shall not become effective unless and until the
Purchaser purchases, pursuant to the Offer, the Securities to which the Required
Consents relate (the date and time of such purchase being referred to herein as
the "Effective Time"). At the Effective Time, the amendments to the Original
Indenture effected hereby, and the release of the Collateral from the Lien of
the Original Indenture and the Securities, shall be deemed fully effective
without any further notice or action on the part of the Company, the Trustee,
the Collateral Agent, any Holder or any other Person.

         SECTION 2.2 Deletion of Certain Definitions. Section 1.1 of the
Original Indenture is amended by deleting in their entirety the following
definitions therefrom, and such definitions shall have no further force or
effect:

<Table>
<S>                                        <C>
"Acquired Indebtedness"                    "Debt Incurrence Ratio"
"Acquisition"                              "Exempted Affiliate Transaction"
"Affiliate Transaction"                    "Existing Agreements"
"Annualized Consolidated EBITDA"           "incur"
"Change of Control"                        "Invested Equity Capital"
"Change of Control Offer"                  "JVI"
"Change of Control Offer Period"           "Non-Domestic Person"
"Change of Control Purchase Date"          "Permitted Lien"
"Change of Control Purchase Price"         "Pledge Agreements"
"Collateral"                               "Pledged Collateral"
"Collateral Agent"                         "Principals"
"Consolidated Cash Flow Ratio"             "Reference Period"
"Consolidated Coverage Ratio"              "Related Party"
"Consolidated Debt"                        "Retained Assets"
</Table>


                                      -3-
<PAGE>

<Table>
<S>                                        <C>
"Consolidated EBITDA"                      "Restricted Investment"
"Consolidated Fixed Charges"               "Significant Subsidiary"
"Consolidated Invested Equity Capital"     "Sun Cable Facility"
"Consolidated Net Income"                  "UIPI"
"Consolidated Subsidiary"                  "Unrestricted Investment"
"Consolidation"                            "UPC"
</Table>

         All references in the Original Indenture and the Securities to the
definitions deleted by this Section 2.2 shall also be deemed deleted, and shall
have no further force or effect.

         SECTION 2.3 Amendments to Certain Definitions.

                  (a) The definition of "Affiliate" in Section 1.1 of the
         Original Indenture is amended and restated to read in its entirety as
         follows:

                  ""Affiliate" means any Person directly or indirectly
         controlling or controlled by or under direct or indirect common control
         with the Company. For purposes of this definition, "control" means the
         power to direct the management and policies of a Person, directly or
         through one or more intermediaries, whether through the ownership of
         voting securities, by contract, or otherwise."

                  (b) The definition of "Indenture" in Section 1.1 of the
         Original Indenture is amended and restated to read in its entirety as
         follows:

                  ""Indenture" means the Original Indenture as amended and
         supplemented by the First Supplemental Indenture, dated as of January
         24, 2002, between the Company and the Trustee, and as further amended
         or supplemented from time to time."

                  All references in the Original Indenture (including references
in the Original Indenture as changed hereby) to "this Indenture" (and indirect
references such as "hereto," "herein," "hereof," "hereby" and "hereunder") shall
be deemed references to the Original Indenture as amended and supplemented
hereby.

         SECTION 2.4 Deletion of Certain Sections. Sections 4.5, 4.6, 4.7, 4.8,
4.9, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16, 4.17 and 4.18 of the Original Indenture
are deleted in their entirety and shall be of no further force or effect. All
references in the Original Indenture and the Securities to any section of the
Original Indenture deleted by this Section 2.4 shall also be deemed deleted, and
shall have no further force or effect.


                                      -4-
<PAGE>

         SECTION 2.5 Termination of Pledge Agreements and Release of Collateral.

                  (a) Article X of the Original Indenture, including Sections
         10.1, 10.2, 10.3, 10.4, 10.5, 10.6, 10.7 and 10.8 thereof, is deleted
         in its entirety and shall be of no further force or effect. All
         references in the Original Indenture and the Securities to Article X,
         or any section thereof, deleted by this Section 2.5 shall also be
         deemed deleted, and shall have no further force or effect.

                  (b) At the Effective Time, and following the taking of such
         action by the Company and the Collateral Agent as may be required of
         either of them under the Termination Agreement or either of the Pledge
         Agreements to terminate any security interests in the Pledged
         Collateral created by the Pledge Agreements or the Original Indenture,
         the Lien on the Collateral created by the Original Indenture and the
         Securities shall be deemed released, and the Company may take
         reassignment and redelivery of the Pledged Collateral from the
         Collateral Agent free of any claim or right of the Trustee or the
         Holders under the Indenture or the Securities.

         SECTION 2.6 Amendments to Sections 4.3 and 4.4. Sections 4.3 and 4.4 of
the Original Indenture are amended and restated to read in their entirety as
follows:

                  "Section 4.3 Reports.

                  The Company shall file with the SEC and provide to the Holders
         and the Trustee, as applicable, the reports, information and documents
         required by TIA Section 314(a).

                  Section 4.4 Compliance Certificate.

                  The Company will deliver to the Trustee within 120 days after
         the end of the Company's fiscal years an Officers' Certificate as
         required by TIA Section 314(a)(4)."

         SECTION 2.7 Amendment to Section 4.10. Clause (vi) of the third
paragraph of Section 4.10 of the Original Indenture is amended and restated to
read in its entirety as follows:

                  "(vi) the Company and its Subsidiaries may exchange all or a
         portion of its property, businesses or assets for Permitted Investments
         or for property, businesses or assets of a type used in a Related
         Business, or a combination of any such Permitted Investments, property,
         businesses or assets; provided that any Cash or Cash Equivalents
         received pursuant to any such exchange shall be applied in the manner
         applicable to Net Cash Proceeds from an Asset Sale as set forth
         pursuant to the provisions of the immediately preceding provisions of
         this Section 4.10."

                  Except as otherwise provided in this Section 2.7, all of the
terms and provisions of Section 4.10 of the Original Indenture shall remain in
full force and effect.


                                      -5-
<PAGE>

         SECTION 2.8 Amendments to Article V. Sections 5.1 and 5.2 of the
Original Indenture are amended and restated to read in their entirety as
follows:

                  "Section 5.1 Limitation On Merger, Sale Or Consolidation.

                  The Company shall not consolidate with or merge with or into
         another Person or, directly or indirectly, sell, lease, convey or
         transfer all or substantially all of its assets (computed on a
         consolidated basis), whether in a single transaction or a series of
         related transactions, to another Person or group of affiliated Persons
         or adopt a Plan of Liquidation, unless either (i) the Company is the
         continuing entity or (ii) the resulting, surviving or transferee entity
         or, in the case of a Plan of Liquidation, the entity which receives the
         greatest value from such Plan of Liquidation is any legal entity formed
         under the laws of any country or any other jurisdiction and expressly
         assumes by supplemental indenture all of the obligations of the Company
         in connection with the Senior Notes and the Indenture.

                  Section 5.2 Successor Entity Substituted.

                  Upon any consolidation or merger or any sale, lease,
         conveyance or transfer of all or substantially all of the assets of the
         Company or consummation of a Plan of Liquidation in accordance with the
         foregoing, the successor entity formed by such consolidation or into
         which the Company is merged or to which such transfer is made or, in
         the case of a Plan of Liquidation, the entity which receives the
         greatest value from such Plan of Liquidation, shall succeed to, and be
         (except in the case of a lease) substituted for, and may exercise every
         right and power of, the Company under the Indenture with the same
         effect as if such successor entity had been named therein as the
         Company, and (except in the case of a lease) the Company shall be
         released from the obligations under the Senior Notes and the Indenture
         except with respect to any obligations that arise from, or are related
         to, such transaction.

                  For purposes of the foregoing, the transfer (by lease,
         assignment, sale or otherwise) of all or substantially all of the
         properties and assets of one or more Subsidiaries or Restricted
         Affiliates, the Company's interest in which constitutes all or
         substantially all of the properties and assets of the Company shall be
         deemed to be the transfer of all or substantially all of the properties
         and assets of the Company."

         SECTION 2.9 Amendments to Sections 6.1 and 6.2. Sections 6.1 and 6.2 of
the Original Indenture are amended and restated to read in their entirety as
follows:

                  "Section 6.1 Events of Default.

                  (a) the Company defaults in the payment of any installment of
         interest when due and the continuance of such default for 30 days;


                                      -6-
<PAGE>

                  (b) the Company defaults in the payment when due of the
         principal, or Accreted Value (as applicable), or premium of the
         Securities, at maturity, upon acceleration, repurchase or otherwise;

                  (c) the Company fails to comply with any of the provisions of
         Section 4.10 hereof with respect to the repurchase of the Securities;

                  (d) [Intentionally deleted.]

                  (e) [Intentionally deleted.]

                  (f) [Intentionally deleted.]

                  (g) the Company pursuant to or within the meaning of
         Bankruptcy Law:

                           (i) commences a voluntary case,

                           (ii) consents to the entry of an order for relief
                  against it in an involuntary case,

                           (iii) consents to the appointment of a Custodian of
                  it or for all or substantially all of its property,

                           (iv) makes a general assignment for the benefit of
                  its creditors, or

                           (v) generally is not paying its debts as they become
                  due; or

                  (h) a court of competent jurisdiction enters an order or
         decree under any Bankruptcy Law that:

                           (i) is for relief against the Company in an
                  involuntary case;

                           (ii) appoints a Custodian of the Company for all or
                  substantially all of the property of the Company; or

                           (iii) orders the liquidation of the Company;

                  and the order or decree remains unstayed and in effect for 60
                  consecutive days; or

                  (i) [Intentionally deleted.]

                  Section 6.2 Acceleration.

                  If any Event of Default (other than an Event of Default
         specified in clause (g) or (h) of Section 6.1 hereof with respect to
         the Company) occurs and is continuing, unless the principal of all of
         the Senior Notes shall have already become due and payable, the Trustee
         or the Holders of at least 25% in principal amount at maturity of the
         then outstanding Securities by notice in writing to the Company (and to
         the Trustee if given by Holders) (an "Acceleration Notice") may


                                      -7-
<PAGE>

         declare all Accreted Value, accrued interest and Liquidated Damages, if
         any, thereon the Securities to be due and payable immediately. Upon any
         such declaration, the Accreted Value of the Securities shall become due
         and payable immediately. Notwithstanding the foregoing, if an Event of
         Default specified in clause (g) or (h) of Section 6.1 hereof occurs
         with respect to the Company all Accreted Value, accrued interest and
         Liquidated Damages, if any, thereon shall be due and payable
         immediately without further action or notice. The Holders of a majority
         in aggregate principal amount at maturity of the then outstanding
         Securities by written notice to the Trustee may on behalf of all of the
         Holders rescind an acceleration and its consequences if the rescission
         would conflict with any judgment or decree and if all existing Events
         of Default (except nonpayment of principal, interest, or premium or
         Liquidated Damages, if any, that has become due solely because of the
         acceleration and except on default with respect to any provision
         requiring a super-majority approval to amend, which default may only be
         waived by such a super-majority) have been cured or waived. Except as
         provided below in the following paragraph, in the event of any such
         acceleration of Securities, the Company will become obligated to pay
         the Accreted Value, plus all applicable premiums, accrued interest and
         Liquidated Damages, of the Senior Notes immediately.

                  The Holders of a majority in aggregate principal amount at
         maturity of the Senior Notes at any time outstanding may waive on
         behalf of all the Holders any default, except a default with respect to
         any provision requiring a super-majority approval to amend, which
         default may only be waived by such a super-majority, and except a
         default in the payment of principal of, Accreted Value, or interest or
         Liquidated Damages on any Senior Note not yet cured or a default with
         respect to any covenant or provision which cannot be modified or
         amended without the consent of the Holder of each outstanding Senior
         Note affected. Subject to Article 7, the Trustee will be under no
         obligation to exercise any of its rights or powers under the Indenture
         at the request, order or direction of any of the Holders, unless such
         Holders have offered to the Trustee reasonable security or indemnity.
         Subject to all provisions of the Indenture and applicable law, the
         Holders of a majority in aggregate principal amount, at maturity, of
         the Senior Notes at the time outstanding will have the right to direct
         the time, method and place of conducting any proceeding for any remedy
         available to the Trustee, or exercising any trust or power conferred on
         the Trustee."

                                  ARTICLE III

                    WAIVER OF DEFAULTS AND EVENTS OF DEFAULT

         SECTION 3.1 Effectiveness. The waivers set forth in this Article III
shall become effective upon the execution of this Supplemental Indenture by the
Company and the Trustee, acting through USBT, on the date hereof.
Notwithstanding the foregoing, the waivers set forth in this Article III shall
cease to be operative, ipso facto and without any further notice or action on
the part of the Company, the Trustee, the Collateral Agent, any Holder or any
other Person, if (i) the Purchaser does not purchase the Securities to which the
Required Consents relate pursuant to


                                      -8-
<PAGE>

the Offer or (ii) the Purchaser terminates the Offer without purchasing the
Securities to which the Required Consents relate.

         SECTION 3.2 Waivers. Pursuant to and in accordance with Section 6.4 and
Section 9.2 of the Original Indenture, the Holders of at least 66 2/3% in
principal amount at maturity of the outstanding Securities (including consents
obtained in connection with the Offer) on the date hereof have consented to:

                  (a) the waiver of any existing Default or Event of Default
         under the Indenture, the Pledge Agreements or the Securities (other
         than a Default or Event of Default in the payment of the principal of,
         Accreted Value, or premium, interest or Liquidated Damages, if any, on
         the Securities) that has or may have occurred at any time prior to
         January 14, 2002;

                  (b) the waiver of any Default or Event of Default under the
         provisions of Article IV, Article VI and Article X of the Original
         Indenture deleted by this Supplemental Indenture or under the Pledge
         Agreements (other than a Default or Event of Default in the payment of
         the principal of, Accreted Value, or premium, interest or Liquidated
         Damages, if any, on the Securities) that occurs or may occur at any
         time on or after January 14, 2002 through the Effective Time; and

                  (c) the waiver of compliance by the Company with any of the
         provisions of Article IV, Article VI and Article X of the Original
         Indenture deleted by this Supplemental Indenture and with the Pledge
         Agreements, at any time on or after January 14, 2002 through the
         Effective Time.

                                   ARTICLE IV

                            MISCELLANEOUS PROVISIONS

         SECTION 4.1 Concerning the Trustee. The Trustee assumes no duties,
responsibilities or liabilities by reason of this Supplemental Indenture, other
than as set forth herein and in the Original Indenture.

         SECTION 4.2 Original Indenture Confirmed and Ratified. Except for the
changes provided for in this Supplemental Indenture and waiver set forth in
Article III, all of the terms and provisions of the Original Indenture and the
Securities shall remain in full force and effect and are hereby approved,
ratified and confirmed.

         SECTION 4.3 Severability. In case any provision in this Supplemental
Indenture or in the Securities 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.

         SECTION 4.4 Governing Law. This internal laws of the State of New York
shall govern and be used to construe this Supplemental Indenture.

         SECTION 4.5 Table of Contents, Headings, etc. The Table of Contents and
Headings of the Articles and Sections of this Supplemental Indenture have been
inserted for convenience of


                                      -9-
<PAGE>

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.

         SECTION 4.6 Counterparts. This Supplemental Indenture may be executed
in any number of counterparts, each of which shall be deemed to be an original
for all purposes, but such counterparts shall together be deemed to constitute
but one and the same instrument.


                                      -10-
<PAGE>

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

                                          UNITEDGLOBALCOM, INC.


                                          By: /s/ Michael T. Fries
                                              ----------------------------------
                                              Name:  Michael T. Fries
                                                    ----------------------------
                                              Title: President
                                                     ---------------------------

ATTEST:

/s/ Ellen P. Spangler
-----------------------------------
Name:  Ellen P. Spangler
      -----------------------------
Title: Senior Vice President and
       Secretary
       ----------------------------
                                          U.S. BANK TRUST NATIONAL ASSOCIATION,
                                          as agent for Firstar Bank, N.A.,
                                          as Indenture Trustee


                                          By: /s/ Kenneth D. Hoffman
                                              ----------------------------------
                                              Name:  Kenneth D. Hoffman
                                                    ----------------------------
                                              Title: Vice President
                                                     ---------------------------

ATTEST:

/s/ Clark Whitmore
-----------------------------------
Name:  Clark Whitmore
      -----------------------------

                                      -11-