Document:

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                                                                    Exhibit 10.5

               Confidential treatment has been requested for portions of this
               exhibit. The copy filed herewith omits the information subject to
               the confidentiality request. Omissions are designated as [*]. A
               complete version of this exhibit has been filed separately with
               the Securities and Exchange Commission.

January 7, 2002

Mr. Morgan Guenther
Senior Vice President, Business Development
TiVo, Inc.
2160 Gold Street
PO Box 2160
Alviso, CA  95002

References: Letter Agreement between TiVo, Inc. and DIRECTV, Inc. dated
            September 28, 2001 (the "Buy-Down Agreement")
            Warrant and Registration Rights Agreement between TiVo, Inc. and
            DIRECTV, Inc. dated October 6, 2000 (the "Warrant Agreement")
            Marketing Agreement between TiVo, Inc. and DIRECTV, Inc. dated April
            13, 1999 the "Marketing Agreement")

Dear Morgan:

This letter amends and supplements the Buy-Down Agreement, which previously
amended and supplemented both the Warrant Agreement and Marketing Agreement.

     1. The third paragraph in Section 2 ("DIRECTV/TiVo Buy-Down Contribution")
     of the Buy-Down Agreement is hereby deleted in its entirety and replaced in
     its entirety with the following paragraph:

          "Following the Term (January 31, 2002) and through March 15, 2002,
          DIRECTV agrees to contribute [*] and TiVo agrees to contribute [*] for
          each DIRECTV with TiVo receiver sold by all authorized DIRECTV dealers
          ("Reno Box"). After March 15, 2002 through [*], TiVo will have no
          obligation to contribute any Buy Down funds for the sale of DIRECTV
          with TiVo combination boxes."

     2. A new third paragraph shall be added to Section 3 ("Consideration to
     DIRECTV") which shall read as follows:

          " - In the event DIRECTV contributes to the buy-down for any DIRECTV
          with TiVo receivers after the March 15, 2002 through [*] in addition
          to the current [*] TiVo revenue share paid to DIRECTV, TiVo will pay
          DIRECTV an incremental revenue share of [*] (for a total of [*]) with
          respect to each receiver for which DIRECTV provides a buy-down
          contribution after the March 15, 2002 date and through [*]. This
          consideration shall replace the previous TiVo warrant structure

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[*] Certain information on this page has been omitted and filed separately with
the Securities and Exchange Commission. Confidential treatment has been
requested with respect to the omitted portions.

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          and TiVo shall not be obligated to contribute a buy-down payment after
          the March 15, 2002 date through [*]."

     3. In the last sentence of the last paragraph of Section 5
     "Administration", the word "TiVo" shall be replaced with the word
     "DIRECTV".

     4. Immediately upon execution of the letter dated January 7, 2002, DIRECTV
     shall communicate to authorized DIRECTV dealers the extension of the
     Buy-Down program through approximately [*].

     5. Except as otherwise set forth above, the terms and conditions of the
     Buy-Down Agreement remain in full force and effect.

Please indicate TiVo's agreement to the above by signing this letter amending
the Buy-Down Agreement as indicated below.

DIRECTV, Inc.

By:    /s/ Larry N. Chapman
       --------------------
Name:  Larry N. Chapman
Title: Executive Vice President

ACKNOWLEDGED AND AGREED:
TiVo, Inc.

By:    /s/ Morgan Guenther                                   Date: 01/07/02
       -------------------                                         --------
Name:  Morgan Guenther
Title: President

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[*] Certain information on this page has been omitted and filed separately with
the Securities and Exchange Commission. Confidential treatment has been
requested with respect to the omitted portions.<PAGE>

                                                                    Exhibit 10.6

               Confidential treatment has been requested for portions of this
               exhibit. The copy filed herewith omits the information subject to
               the confidentiality request. Omissions are designated as [*]. A
               complete version of this exhibit has been filed separately with
               the Securities and Exchange Commission.

          Amendment to Marketing Agreement and Tax Agreement

Whereas, DIRECTV, Inc. ("DIRECTV") and TiVo, Inc. ("TiVo") previously entered
into, among other agreements, that certain Marketing Agreement dated as of April
13, 1999 (the "Marketing Agreement"), and that certain Letter Agreement dated as
of July 24, 2001 Re: Taxation of TiVo Services that are billed by DIRECTV (the
"Tax Agreement");

Whereas, the parties are executing on this date a Development Agreement
("Development Agreement") and a Services Agreement ("Services Agreement"), and
the parties contemplate that, pursuant to the Development Agreement, upon
DIRECTV's request they shall also enter into an Intellectual Property and
Technology License Agreement ("License Agreement");

Whereas, the parties desire to reflect certain changes to the Marketing
Agreement, and in connection with the execution of the Development Agreement and
Services Agreement, the parties intend to modify certain provisions of the
Marketing Agreement and the Tax Agreement;

Now therefore, DIRECTV and TiVo hereby agree as follows:

I.   The Marketing Agreement is hereby amended as follows:

     A.   Billing System.
          --------------

          1.   Section 2.3 of the Marketing Agreement is hereby amended and
               replaced in its entirety to reflect that DIRECTV shall continue
               to undertake the billing and remittance processing activities
               relating to the sale of the TiVo Service to DIRECTV/TiVo
               Subscribers using the DIRECTV/TiVo Combo Receiver, in the manner
               mutually agreed upon by the parties, as provided to date. TiVo
               shall remain solely responsible for billing and remittance
               processing activities relating to the sale of the TiVo Service to
               TiVo subscribers using the TiVo Stand-Alone Receiver.

          2.   The provisions of Section 4.1 of the Development Agreement shall
               supercede and replace said Section 2.3 of the Marketing
               Agreement, effective immediately after the Transition Date (as
               defined in the Marketing Agreement).

     B.   Customer Service. The provisions of Section 4.2 of the Development
          ----------------
          Agreement shall supercede and replace Section 2.4 of the Marketing
          Agreement, with respect to DIRECTV/TiVo Combo Receivers (as defined in
          the Marketing Agreement).

     C.   Customer Data. Section 2.9 of the Marketing Agreement is replaced and
          -------------
          superceded by Section 4.4 of the Development Agreement.

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     D.   Bandwidth Allocation.
          ---------------------

          1.   Upon satisfaction and cancellation of the promissory note as
               referenced in Schedule 5.1.2 of the Marketing Agreement, DIRECTV
               shall be relieved of any Bandwidth Capacity obligations under the
               Marketing Agreement. This shall not affect any other bandwidth
               obligations in other agreements.

          2.   Section 2.2(e) of the Services Agreement shall supersede and
               replace Section 3.0 of the Marketing Agreement, effective as of
               the Manufacturing Release of the Provo Receiver, as provided in
               said Section 2.2(e).

     E.   Revenue Sharing.
          ----------------

          1.   Section 4.1.2 of the Marketing Agreement is hereby replaced in
               its entirety with the following:

          4.1.2 Permanent Revenue Share for TiVo Stand-Alone Receiver. TiVo
                -----------------------------------------------------
               shall pay DIRECTV on a monthly basis, [*] of Stand-Alone Revenue
               Attributable to DIRECTV (as defined below, and determined as of
               the Calculation Date), with a [*] (the "Stand-Alone Receiver
               Revenue Share"). TiVo shall pay DIRECTV the Stand-Alone Revenue
               Share within thirty (30) days of each Calculation Date.
               "Stand-Alone Revenue Attributable to DIRECTV" shall be defined
               as, for any particular month, an amount equal to the total
               subscription revenue received by TiVo during such month for
               subscription fees paid for the TiVo Service (including all
               subscription fees received for subscription to the TiVo Service
               for terms longer than one (1) month) for all DIRECTV/TiVo
               Subscribers utilizing the TiVo Stand-Alone Receiver (as
               determined by the number of TiVo Stand-Alone Receivers which
               "self-report" the use of the DIRECTV head-end during TiVo Service
               set-up).

          2.   Section 4.1.3 of the Marketing Agreement shall terminate.

     F.   TiVo Promotional Activities. Section 4.2 of the Marketing Agreement
          ---------------------------
          shall terminate as of the Manufacturing Release of the Version [*]
          Software (as provided in the Development Agreement).

     G.   Calculation of DIRECTV/TiVo Subscribers. Section 4.3 of the Marketing
          ---------------------------------------
          Agreement shall terminate.

     H.   Audit Rights. Section 4.4 of the Marketing Agreement is hereby amended
          ------------
          and replaced to read as follows:

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[*] Certain information on this page has been omitted and filed separately with
the Securities and Exchange Commission. Confidential treatment has been
requested with respect to the omitted portions.

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     4.4 Audit Rights. No more than once every year during the Term and for one
         ------------
     year thereafter, DIRECTV or its designee (which designee shall be subject
     to approval by TiVo and appropriate confidentiality requirements) shall
     have the right upon twenty (20) days' notice and during regular business
     hours at TiVo's regular locations for maintenance of such records, to
     conduct an audit of such records (which records shall be maintained for at
     least 18 months by TiVo) as are necessary to verify compliance with the
     Agreement. If any such audit should disclose any underpayments of revenue
     share or other fees, TiVo shall promptly pay to DIRECTV such underpaid
     amount, together with interest at a rate of 18% per annum or the highest
     rate allowed by law, during such period which such amount became due until
     finally paid. If any such audit should disclose any overpayments of revenue
     share or other fees, TiVo shall have the right to offset any such amounts
     against future amounts payable by TiVo hereunder; provided that if the
     overpayment exceeds five percent (5%) in any calendar quarter, such offset
     shall be reduced by one-half of the reasonable costs and expenses incurred
     by DIRECTV in connection with such audit. The audit will be conducted at
     DIRECTV's expense, except as otherwise provided above and unless the audit
     reveals that TiVo has underpaid DIRECTV by five percent (5%) or more in any
     calendar quarter, in which case TiVo will reimburse DIRECTV for all
     reasonable costs and expenses incurred by DIRECTV in connection with such
     audit.

     I.   Indemnification and Limitation of Liability. The provisions of
          -------------------------------------------
          Sections 10.1, 10.2 and 10.3 of the Marketing Agreement shall be
          superseded and terminate, solely with respect to the DIRECTV-TiVo
          Combo Receiver, upon the execution of the Technology License
          Agreement.

     J.   Schedule 6. Until the date that is 4 weeks following the initiation of
          ----------
          the download of the Version [*] Software to the Reno Receivers as
          provided in the Development Agreement, Section 2 (Promotional
                                                            -----------
          Showcases) to Schedule 6 of the Marketing Agreement shall remain in
          ---------
          full force and effect. Following such date, Section 2 to Schedule 6
          shall be superseded in its entirety by the Services Agreement.

II.  The Tax Agreement is hereby amended as follows:

     The indemnity obligations of TiVo set forth in the final paragraph of the
     Tax Agreement shall continue to apply with respect to the taxation of any
     TiVo Services for which DIRECTV has provided and continues to provide
     billing services until the Transition Date, as specified in Section 4.1 of
     the Development Agreement. Immediately after the Transition Date, DIRECTV
     shall have responsibility for the Taxability Determinations (as defined in
     the Tax Agreement) as applicable to the TiVo Services for which DIRECTV
     provides billing services thereafter, and DIRECTV shall indemnify, defend
     and hold harmless TiVo for any

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[*] Certain information on this page has been omitted and filed separately with
the Securities and Exchange Commission. Confidential treatment has been
requested with respect to the omitted portions.

<PAGE>

     liability for uncollected taxes, interest and penalties resulting from any
     error or omission in the Taxability Determinations occurring after the
     Transition Date.

III. The parties further agree that they shall cooperate in good faith to
     promptly document and clarify any further changes or amendments to the
     agreements executed prior to the Development Agreement and Services
     Agreement as necessary to reflect their mutual understanding and intention
     regarding the modifications to the parties' relationship resulting from the
     Development Agreement, Technology License Agreement and Services Agreement.

IV.  Except as expressly set forth herein or as otherwise provided by written
     mutual agreement of the parties, all terms and conditions of the Marketing
     Agreement and Tax Agreement shall remain in full force and effect,
     enforceable in accordance with the terms thereof. Any capitalized terms not
     defined in this Amendment shall have the meaning set forth in the
     Development Agreement or Services Agreement, as applicable.

                      This space intentionally left blank.

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IN WITNESS WHEREOF, the parties have executed this Amendment to the
Marketing Agreement and Tax Agreement as of the 15th day of February, 2002.

TiVo Inc.                                  DIRECTV, Inc.

By:    /s/ Morgan Guenther                 By:   /s/ Larry N. Chapman
       -------------------                       -------------------------------
Name:  Morgan Guenther                     Name: Larry N. Chapman
Title: President                                 Title: Executive Vice President

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