<PAGE>   1
                                                                   EXHIBIT 10.55

                                                             [Form of Agreement]

                           TCI INTERNET SERVICES, INC.

                            STOCK APPRECIATION RIGHT


               THIS AGREEMENT ("AGREEMENT") is made as of the 1ST DAY OF
DECEMBER, 1996, by and among TCI INTERNET SERVICES, INC., a Colorado corporation
(the "COMPANY"), and TELE-COMMUNICATIONS, INC., a Delaware corporation ("TCI"),
and [ ] ("GRANTEE").

               The Company is on the date hereof a Subsidiary of TCI. The Board
of Directors of the Company ("COMPANY BOARD") and the Board of Directors of TCI
have each determined that it is in the best interests of the Company and TCI to
grant Grantee the stock appreciation rights set forth herein in order to provide
Grantee with additional remuneration for services rendered to the Company and
its predecessors, to encourage Grantee to remain in the employ of TCI and/or one
or more of its Subsidiaries, including the Company, and to provide additional
incentive to Grantee by increasing Grantee's proprietary interest in the
continued success and progress of the Company. Capitalized terms used herein and
not otherwise defined are defined in paragraph 18 below.

               Accordingly, the Company, Grantee and, for purposes of paragraph
5 only, TCI hereby agree as follows:

         1.    GRANT OF STOCK APPRECIATION RIGHTS; TERM. (a) The Company hereby
grants to Grantee stock appreciation rights ("SARS") with respect to ten (10)
(the "TOTAL NUMBER OF SARS") shares of Company Common Stock on the terms and
subject to the conditions set forth herein. The Total Number of SARs and the
Strike Price are subject to adjustment pursuant to paragraph 9 below. Subject to
paragraph 2, the SARs shall be exercisable in whole at any time and in part from
time to time during the period commencing on the date hereof and expiring at
5:00 p.m., Denver, Colorado time ("CLOSE OF BUSINESS") on the tenth anniversary
of the Determination Date, or such earlier date as the SARs may be terminated
pursuant to paragraph 6 or paragraph 9(c) (the "TERM").

               (b) The grant of SARs hereunder, together with the grant of the 
TCI.NET Option (as defined below), shall be deemed to be in substitution for and
replacement of the options to purchase Company Common Stock which were
previously granted by the Company to Grantee, and the parties acknowledge and
agree that such prior option grant is hereby terminated and shall cease to be of
any further force and effect.

         2.    CONDITIONS OF EXERCISE; VESTING. Except as otherwise provided in 
the last sentence of this paragraph 2 or in paragraph 9(c), the SARs shall not
be exercisable until the first anniversary of the Determination Date, and, from
the first anniversary of the Determination Date to the fifth anniversary of the
Determination Date, the SARs shall vest and become exercisable in accordance
with the following schedule:



<PAGE>   2

<TABLE>
<CAPTION>
     Anniversary of                    Percentage of Total Number
    Determination Date                     of SARs Exercisable
    ------------------                 --------------------------
<S>                                                <C>
            1st                                      20%
            2nd                                      40%
            3rd                                      60%
            4th                                      80%
            5th                                     100%
</TABLE>

         Notwithstanding the foregoing, all then unexercised SARs (the
"REMAINING SARS") shall become exercisable if during the Term (i) Grantee's
employment with the TCI Group shall terminate by reason of (x) termination by
the TCI Group without Cause, (y) termination by Grantee for Good Reason or (z)
Disability, (ii) Grantee's employment shall terminate pursuant to provisions of
a written employment agreement, if any, between Grantee and the applicable
member(s) of the TCI Group which expressly permits Grantee to terminate such
employment upon the occurrence of specified events (other than the giving of
notice and passage of time) or (iii) Grantee dies while employed by the TCI
Group. A change of employment is not a termination of employment within the
meaning of this paragraph 2, provided that, after giving effect to such change,
Grantee is an employee of, or becomes or continues to be a consultant to, any
member of the TCI Group.

         3.    EXERCISE OF SARS; SUBSEQUENT RESCISSION. (a) SARs granted 
hereunder may be exercised by delivery to the Company of a written notice (the
"EXERCISE NOTICE") specifying the whole number of SARs being exercised. So long
as the Company and TCI.NET, Inc. ("TCI.NET") are both Subsidiaries of TCI, it
shall be a condition to a valid exercise of SARs that such notice also contain
evidence satisfactory to the Company Board that Grantee is validly and
simultaneously exercising the same proportion of the stock option (the "TCI.NET
OPTION") granted to him by TCI.NET pursuant to that certain option agreement,
dated as of the date hereof, among TCI.NET, Grantee and TCI, as the same may
hereafter be amended, modified or supplemented from time to time. The date upon
which such notice is validly delivered to the Company shall be deemed to be the
date of exercise of the SARs specified therein (the "EXERCISE DATE"). Upon the
valid exercise of SARs (which exercise is not subsequently rescinded as provided
herein) Grantee shall be entitled to receive from the Company, with respect to
each SAR then being exercised, the excess of (i) the Per Share Value of a share
of Company Common Stock as of the Exercise Date over (ii) the Strike Price
applicable as of such Exercise Date (such excess, the "CASH VALUE").

               (b) Grantee shall have the right to rescind an exercise of SARs
(which rescission will also constitute a rescission of the corresponding
exercise of the TCI.NET Option) prior to the Close of Business on the fifteenth
(15th) day following the Exercise Date in the event that (i) Grantee has elected
to determine the Per Share Value through negotiation with the Company, (ii)
Grantee and the Company have not agreed upon a Per Share Value by such date and
(iii) Grantee has not made a subsequent election to require that the Per Share
Value be determined by appraisal pursuant to paragraph 10(c) hereof. In
addition, an exercise of SARs shall be deemed rescinded under the circumstances
set forth in paragraph 10(b) hereof. In the event of any rescission of an








                                       2
<PAGE>   3


exercise of SARs pursuant to this paragraph 3(b), Grantee shall not be permitted
to again exercise SARs for a period of thirty (30) days following the date of
such rescission.

               (c) In the event the Grantee elects to rescind his exercise of
SARs, such exercise shall be deemed rescinded ab initio and the future
exercisability and vesting of those SARs whose exercise has been rescinded shall
not be affected by such exercise and subsequent rescission, except as provided
in the last sentence of paragraph 3(b) above.

         4.    WITHHOLDING FOR TAXES. It shall be a condition precedent to any
exercise of a SAR that Grantee make provision acceptable to the Company for the
payment or withholding of any and all federal, state and local taxes required to
be withheld by the Company to satisfy the tax liability associated with such
exercise, as determined by the Company Board.

         5.    DELIVERY BY THE COMPANY. (a) Subject to the withholding referred
to in paragraph 4, the Company shall deliver or cause to be delivered to Grantee
the Cash Value of the SARs then being exercised, with such amount being paid, at
the Company's election, in (i) cash, (ii) provided that the Company is then a
Public Company and that the Company Common Stock is then listed or traded on
NASDAQ or a national securities exchange and is actively traded, shares of
Company Common Stock, (iii) shares of Tele-Communications, Inc. Series A TCI
Group Common Stock, $1.00 par value per share, or any successor class or series
of TCI's common stock, or if any class or series of TCI's common stock is
hereafter created that is intended to track the separate performance of
specified assets or businesses of TCI that include assets and businesses of the
Company, shares of such class or series (and if more than one series of such
"tracking stock" is created with different voting rights, the series with the
lower voting rights), provided that shares of the same class and series of
securities being so delivered are then listed or traded on NASDAQ or a national
securities exchange and are actively traded (collectively, the "TCI STOCK"), or
(iv) any combination of cash, Company Common Stock and TCI Stock as the Company
may elect. It shall be a condition to the Company's right to deliver shares of
Company Common Stock or TCI Stock in satisfaction of its obligations hereunder
that (i) the issuance of such shares to Grantee shall have been registered under
the Securities Act of 1933, as amended (the "SECURITIES ACT"), on Form S-8 (or
other appropriate form) and (ii) such shares may be immediately sold in the
market by Grantee (either pursuant to Rule 144 or a resale prospectus prepared
by the Company or TCI, as the case may be). If the Company elects to pay all or
any portion of the Cash Value in shares of Company Common Stock or TCI Stock,
said shares shall be valued for such purpose at the most recent Closing Price
thereof as of the date of delivery of such shares to Grantee. The payment of the
Cash Value (in cash or by delivery of Company Common Stock or TCI Stock) shall
be made (i) if the Company is a Public Company, on the 10th day following the
Exercise Date and (ii) if the Company is not a Public Company, on the 10th day
following either (x) the date Grantee and the Company mutually agree as to the
Agreed Per Share Value or (y) the receipt by Grantee and the Company of notice
pursuant to paragraph 10(c) of the final determination of the Appraised Per
Share Value (or on such other date as the parties may agree). Upon an election
to pay all or a portion of the Cash Value in shares of Company Common Stock or
TCI Stock, the Company or TCI, as applicable, shall enter into a registration
rights agreement with Grantee, providing Grantee registration rights with
respect

 
                                        3

<PAGE>   4



to the shares so delivered on the terms and subject to the conditions contained
in the Company's or TCI's standard form of such agreement and with such
variations as the parties agree.

               (b) To the extent Grantee so requests in the Exercise Notice, the
Company agrees that it will pay in cash to TCI.NET, on behalf of Grantee, a
specified amount of the Cash Value payable to Grantee upon exercise of SARs in
payment of the applicable exercise price of the TCI.NET Options then being
exercised by Grantee.

               (c) TCI hereby covenants and undertakes to cause the Company to
comply with its covenants, agreements and obligations hereunder to the same
extent as if such covenants, agreements and obligations were binding upon TCI;
provided, that TCI's obligations hereunder shall terminate (to the extent not
fixed and accrued) at such time as the Company ceases to be a Subsidiary of TCI.

         6.    EARLY TERMINATION OF SARS. Unless otherwise determined by the
Company Board in its sole discretion, the SARs shall terminate prior to the
expiration of the ten-year period provided for in paragraph 1, as follows:

               (a) If Grantee's employment with the TCI Group terminates other
         than (i) by Grantee with Good Reason, (ii) by reason of Grantee's death
         or Disability, (iii) with the written consent of the applicable
         member(s) of the TCI Group, (iv) without such consent if such
         termination is pursuant to provisions of a written employment
         agreement, if any, between Grantee and the applicable member(s) of the
         TCI Group which expressly permits Grantee to terminate such employment
         upon the occurrence of specified events (other than the giving of
         notice and passage of time), or (v) by the TCI Group with or without
         Cause, then the SARs shall terminate at the Close of Business on the
         first business day following the expiration of the 90-day period
         beginning on the date of termination of Grantee's employment;

               (b) If Grantee dies (i) while employed by the TCI Group or (ii)
         prior to the expiration of a relevant period of time following
         termination of employment during which the SARs remain exercisable as
         provided in this paragraph 6, the SARs shall terminate at the Close of
         Business on the first business day following the expiration of the
         one-year period beginning on the date of death;

               (c) If Grantee's employment with the TCI Group terminates by
         reason of Disability, then the SARs shall terminate at the Close of
         Business on the first business day following the expiration of the
         one-year period beginning on the date of termination of Grantee's
         employment;

               (d) If Grantee's employment with the TCI Group is terminated by
         the TCI Group for Cause, then the SARs shall terminate immediately upon
         such termination of Grantee's employment; and

 
                                        4

<PAGE>   5



               (e) If Grantee terminates his employment with the TCI Group (i)
         with Good Reason, (ii) with the written consent of the applicable
         member(s) of the TCI Group or (iii) pursuant to provisions of a written
         employment agreement, if any, between Grantee and the applicable
         member(s) of the TCI Group which expressly permits Grantee to terminate
         such employment upon the occurrence of specified events (other than the
         giving of notice and passage of time), or if the TCI Group terminates
         Grantee's employment with the TCI Group without Cause, then the Term
         shall not terminate prior to the end of the ten-year period provided
         for in paragraph 1, except as otherwise provided for in paragraph 6(b)
         or 9(c).

         In any event in which the SARs remain exercisable for a period of time
following the date of termination of Grantee's employment as provided above,
such SARs may be exercised during such period of time only to the extent they
were exercisable as provided in paragraph 2 or paragraph 9(c) on such date of
termination of Grantee's employment. A change of employment is not a termination
of employment within the meaning of this paragraph 6, provided that, after
giving effect to such change, Grantee is an employee of, or becomes or continues
to be a consultant to, any member of the TCI Group. Anything contained herein to
the contrary notwithstanding, the SARs shall in any event terminate upon the
expiration of the ten-year period provided for in paragraph 1, if not
theretofore terminated.

         7.    NONTRANSFERABILITY OF SARS. During Grantee's lifetime, the SARs
are not and shall not be transferable (voluntarily or involuntarily) other than
pursuant to a Domestic Relations Order and, except as otherwise required
pursuant to a Domestic Relations Order, the SARs shall be exercisable only by
Grantee or Grantee's court appointed legal representative. Grantee may designate
a beneficiary or beneficiaries to whom the SARs shall pass upon Grantee's death
and may change such designation from time to time by filing a written
designation of beneficiary or beneficiaries with the Company on the form annexed
hereto as Exhibit A or such other form as may be prescribed by the Company
Board, provided that no such designation shall be effective unless so filed
prior to the death of Grantee. If no such designation is made or if the
designated beneficiary does not survive Grantee's death, the SARs shall pass by
will or the laws of descent and distribution. Following Grantee's death, the
SARs, if otherwise exercisable, may be exercised by the person to whom the SARs
pass according to the foregoing, and such person shall be deemed to be Grantee
for purposes of any applicable provisions of this Agreement.

         8.    NO SHAREHOLDER RIGHTS; NO GUARANTEE OF EMPLOYMENT; UNSECURED
OBLIGATION. (a) Grantee shall not be deemed for any purpose to be, or to have
any of the rights of, a stockholder of the Company. The existence of this
Agreement and Grantee's rights hereunder shall not affect in any way the right
or power of the Company or its stockholders to accomplish any corporate act.

               (b) Nothing contained in this Agreement, and no action by the
Company or the Company Board with respect hereto, shall confer or be construed
to confer on Grantee any right to continue in the employ of the TCI Group or any
member thereof or interfere in any way with the right of TCI, the Company or any
employing member of the TCI Group to terminate Grantee's

 
                                        5

<PAGE>   6



employment at any time, with or without Cause, except as otherwise expressly
provided in any written employment agreement between the applicable member(s) of
the TCI Group and Grantee.

               (c) The amount of cash payable at any time by the Company upon
the valid exercise of SARs granted hereunder shall not in any way be reserved or
held in trust by the Company or TCI. Grantee shall not have any rights against
the Company in respect of payments of such amount of cash other than as the
rights of an unsecured general creditor of the Company. The amount of cash
payable upon the valid exercise of SARs hereunder shall not be subject in any
manner to anticipation, alienation, sale, transfer, assignment, pledge,
encumbrance or charge, and shall not in any manner be liable or subject to the
debts, contracts, liabilities, engagements or torts of Grantee or of any
designated beneficiary or personal representative.

         9.    ADJUSTMENTS; ACCELERATION; AUTOMATIC EXERCISE. (a) If, after
December 31, 1996, the Company: (i) pays a dividend or makes a distribution on
the Company Common Stock in shares of Company Common Stock; (ii) subdivides the
outstanding shares of Company Common Stock into a greater number of shares or
(iii) combines the outstanding shares of Company Common Stock into a smaller
number of shares, then the number of Remaining SARs, the number of shares of
Company Common Stock to which such Remaining SARs relate (the "REFERENCE
SHARES") and the Strike Price in effect immediately prior to the opening of
business on the record date for such dividend or distribution or the effective
date of such subdivision or combination, shall be adjusted proportionately so
that the number of SARs and the shares of Company Common Stock to which the SARs
relate will be equal to that number of shares of Company Common Stock which the
Reference Shares would have become had such shares been issued and outstanding
as of the date such adjustment was required to be made. The adjustment
contemplated by the preceding sentence shall be made successively whenever any
event listed above shall occur. For a dividend or distribution, the adjustment
shall become effective immediately after the record date for the dividend or
distribution. For a subdivision or combination, the adjustment shall become
effective immediately after the effective date of the subdivision or
combination. Adjustments to the Strike Price shall be made on a per SAR basis so
that the aggregate Strike Price of all SARs outstanding following such
adjustment is unchanged.

               (b) The SARs shall also be subject to adjustment (including,
without limitation, as to the number of shares of Company Common Stock as to
which the SARs relate and the Strike Price) in the sole discretion of the
Company Board and in such manner as the Company Board may deem equitable and
appropriate in connection with the occurrence of any of the following events
after December 31, 1996 that affects the Company Common Stock such that an
adjustment would be required in order to preserve the benefits or potential
benefits intended to be made available under this Agreement: any dividend or
distribution on the Company Common Stock in shares of the Company's capital
stock (other than Company Common Stock); any reclassification of the Company
Common Stock into shares of the Company's capital stock (other than a
reclassification by way of an Approved Transaction); any extraordinary cash
dividend; any distribution of any rights, warrants or options to holders of
Company Common Stock; any distribution of any assets or debt securities (other
than cash dividends or distributions that are not extraordinary cash dividends);
any


                                        6

<PAGE>   7



recapitalization, reorganization, split up or spin off; and any merger,
consolidation or binding share exchange that reclassifies or changes the
outstanding Company Common Stock or other similar corporate event (other than
those which constitute Approved Transactions). Notwithstanding the foregoing, in
the event of any reclassification or recapitalization of the Company Common
Stock into two or more classes or series of common stock with different voting
rights (however the same may be effected), the SARs shall relate to the shares
of the class or series of common stock of the Company with the fewest number of
votes per share. Adjustments to the Strike Price shall be made on a per SAR
basis so that the aggregate Strike Price of all SARs outstanding following such
adjustment is unchanged.

               (c) The Company Board may at any time in its sole discretion
determine that the SARs shall become exercisable in full, without regard to
paragraph 2, whether immediately, upon the occurrence of specified events, or
otherwise. Without limiting the generality of the foregoing, in the event of any
Board Change, Control Purchase or Approved Transaction that occurs with respect
to TCI following December 31, 1996 and prior to the earlier of such time as the
Company ceases to be a Subsidiary of TCI or such time as the Company becomes a
Public Company, the SARs shall become exercisable in full, without regard to
paragraph 2, effective upon the Board Change or Control Purchase or immediately
prior to consummation of the Approved Transaction, as applicable (or at such
earlier time as the Company Board in its sole discretion may determine);
provided, however, that to the extent not theretofore exercised the SARs shall
terminate upon the first to occur of the consummation of the Approved
Transaction or the expiration or early termination of the Term. In the event
that (i) at any time after December 31, 1996 while the Company is a Subsidiary
of TCI, an Approved Transaction occurs with respect to the Company after giving
effect to which the Company will cease to be a Subsidiary of TCI or (ii) an
Approved Transaction, Board Change or Control Purchase occurs with respect to
the Company at a time following December 31, 1996 that the Company is no longer
a Subsidiary of TCI, then, in any such case, the SARs shall become exercisable
in full, without regard to paragraph 2, effective upon the Board Change or
Control Purchase or immediately prior to consummation of the Approved
Transaction, as applicable (or at such earlier time as the Company Board in its
sole discretion may determine); provided, however, that to the extent not
theretofore exercised the SARs shall terminate upon the first to occur of the
consummation of the Approved Transaction or the expiration or early termination
of the Term. Notwithstanding the foregoing, the Company Board may, in its
discretion, determine that the SARs will not become exercisable on an
accelerated basis in connection with an Approved Transaction and/or will not
terminate if not exercised prior to consummation of the Approved Transaction, if
the Company Board or the surviving or acquiring corporation, as the case may be,
shall have taken or made effective provision for the taking of such action as in
the opinion of the Company Board is equitable and appropriate to substitute new
stock appreciation rights for the SARs evidenced by this Agreement or to assume
this Agreement and the SARs evidenced hereby and in order to make such new or
assumed stock appreciation rights, as nearly as may be practicable, equivalent
to the SARs evidenced by this Agreement as then in effect (but before giving
effect to any acceleration of the exercisability hereof unless otherwise
determined by the Company Board), taking into account, to the extent applicable,
the kind and amount of securities, cash or other assets into or for which the

 
                                        7

<PAGE>   8



Company Common Stock may be changed, converted or exchanged in connection with
the Approved Transaction.

               (d) All actions taken by the Company Board with respect to the
SARs pursuant to this paragraph 9 shall be consistent with any actions taken by
the Company Board with respect to the Other SARs.

               (e) Immediately prior to the termination of the SARs as provided
in paragraph 6 above (other than pursuant to paragraph 6(d)), this paragraph 9,
or the expiration of the Term, all Remaining SARs shall be deemed to have been
exercised by Grantee and Grantee shall be deemed to have taken all actions
required by paragraph 3(a) for a valid exercise of SARs (and, to the extent that
a corresponding exercise of the TCI.NET Option is required pursuant to paragraph
3(a), Grantee shall be deemed to have instructed the Company to pay the exercise
price of the TCI.NET Option to TCI.NET from the proceeds of the exercise of
SARs).

         10.   RESTRICTIONS IMPOSED BY LAW; AGREED PER SHARE VALUE; APPRAISAL
PROCEDURES. (a) Grantee acknowledges that neither the SARs nor the interests
evidenced thereby have been registered under the Securities Act and that neither
the SARs nor such interests may be transferred in the absence of such
registration or the availability of an exemption therefrom under the Securities
Act or the rules and regulations of the Securities and Exchange Commission
promulgated thereunder. Neither the Company nor any other person shall have any
obligation to register the SARs or the interests represented thereby, or any
transfer of the SARs or the interests represented thereby, under the Securities
Act, the Exchange Act or any other state or federal securities law.

               (b) In the event that the Company is not a Public Company as of
the Exercise Date, Grantee shall have the right to elect that the Per Share
Value be determined by appraisal as provided herein or to seek to negotiate a
mutually acceptable Per Share Value with the Company; provided, that in the
event Grantee and the Company are unable to agree upon the Per Share Value prior
to the Close of Business on the fifteenth (15th) day following the Exercise
Date, then Grantee shall have the further right (subject to the last sentence of
paragraph 10(c) below), exercisable by written notice to the Company, to require
that the Per Share Value be determined by appraisal as provided herein. In the
event Grantee and the Company have not agreed upon the Per Share Value as of the
Close of Business on such fifteenth (15th) day and the Grantee has not delivered
notice requiring appraisal, the Grantee shall be deemed to have rescinded the
exercise of SARs pursuant to paragraph 3 hereof. In the event that Grantee
elects to seek to negotiate the Per Share Value with the Company, each party
agrees to negotiate in good faith and use its commercially reasonable efforts to
agree upon the Agreed Per Share Value. The parties acknowledge and agree that in
connection with such negotiations the parties shall give due consideration to
the determination of the Fair Market Value of the Company (as set forth in the
definition thereof) and the number of shares of Company Common Stock outstanding
(based upon the principles set forth in paragraph 10(c) hereof).


 
                                        8

<PAGE>   9



               (c) In the event Grantee elects to require that the Per Share
Value be determined by appraisal, Grantee shall specify in the Exercise Notice
or the subsequent written notice to the Company electing appraisal, the identity
of the Appraiser selected by Grantee to make the determination of the Fair
Market Value of the Company (the "FIRST APPRAISER"). Within three (3) business
days following receipt of such notice, the Company shall notify Grantee in
writing as to the identity of the Appraiser selected by the Company (the "SECOND
APPRAISER"). The First Appraiser and the Second Appraiser shall each submit its
determination of the Fair Market Value of the Company to Grantee and the Company
within thirty (30) days of the date of selection of the Second Appraiser. If the
respective determinations of the Fair Market Value of the Company by such
Appraisers vary by less than 10% of the higher determination, then the Fair
Market Value of the Company shall be the average of the two determinations. If
such determinations vary by 10% or more of the higher determination, the two
Appraisers shall promptly designate a third Appraiser (the "THIRD APPRAISER").
Neither Grantee nor the Company shall provide, and the First Appraiser and
Second Appraiser shall be instructed not to provide, any information to the
Third Appraiser as to the determination of the First Appraiser and Second
Appraiser or otherwise influence such Third Appraiser's determination. The Third
Appraiser shall submit its determination of the Fair Market Value of the Company
to Grantee and the Company within fifteen (15) days of the date of its
selection. The Fair Market Value of the Company shall be equal to the average of
the two closest of the three determinations, provided that, if the difference
between the highest and middle determinations is no more than 105% and no less
than 95% of the difference between the middle and lowest determinations, the
Fair Market Value of the Company shall be equal to the middle determination.
Following the determination of the Fair Market Value of the Company, the
Appraisers whose determinations were used in the calculation of the Fair Market
Value of the Company shall determine the number of shares of Company Common
Stock outstanding together with any further appropriate adjustments to the Fair
Market Value of the Company resulting from such determination. The number of
shares of Company Common Stock outstanding shall mean a number, as determined by
such Appraisers as of the applicable date, equal to the sum of the number of
shares of Company Common Stock outstanding and the number of shares of Company
Common Stock issuable upon the conversion, exercise or exchange of those
convertible securities the holders of which would derive an economic benefit
from the conversion, exercise of exchange of such convertible securities which
exceeds the economic benefits of not converting, exercising or exchanging such
convertible securities. The Appraisers shall then calculate the value per share
of Company Common Stock (the "APPRAISED PER SHARE VALUE"), which shall be the
quotient obtained by dividing the Fair Market Value of the Company by the number
of shares of Company Common Stock outstanding or deemed outstanding; provided,
that if such Appraisers do not agree on the number of shares of Company Common
Stock outstanding, each Appraiser whose determination of the Fair Market Value
of the Company is being used in the calculation of the Appraised Per Share Value
shall determine the Appraised Per Share Value based upon its determination of
the Fair Market Value of the Company and the number of shares of Company Common
Stock outstanding, and the Appraised Per Share Value shall be the average of the
quotients so obtained on the basis of the respective determinations of such
firms. The Appraisers shall jointly notify the Company and Grantee in writing of
their final determination of the Appraised Per Share Value of the Company Common
Stock within five (5) days after the determination of the Fair Market Value of
the

 
                                       9

<PAGE>   10



Company. Grantee and the Company shall each pay the fees and expenses of his or
its own Appraiser and one-half of the fees and expenses of the Third Appraiser,
if any. Grantee acknowledges and agrees that he shall not be entitled to require
an appraisal pursuant to this Agreement more than once in any 12 month period.

         11. NOTICE. Unless the Company or TCI, as applicable, notifies Grantee
in writing of a change of address, any notice or other communication to the
Applicable Person with respect to this Agreement shall be in writing and shall
be delivered personally or sent by first class mail, postage prepaid and
addressed as follows:

                                    If to the Company:

                                    TCI Internet  Services, Inc.
                                    5619 DTC Parkway
                                    Englewood, Colorado 80111
                                    Attention:  General Counsel

                                    If to TCI:

                                    Tele-Communications, Inc.
                                    5619 DTC Parkway
                                    Englewood, Colorado 80111
                                    Attention:  General Counsel

Any notice or other communication by the Company or TCI to Grantee with respect
to this Agreement shall be in writing and shall be delivered personally, or
shall be sent by first class mail, postage prepaid, to Grantee's address as
listed in the records of TCI on the date hereof, unless the Company has received
written notification from Grantee of a change of address. Except as otherwise
specifically provided herein, all notices and other communications hereunder,
including without limitation any Exercise Notice, shall be effective when
actually received.

         12.   GOVERNING LAW. This Agreement shall be governed by, and construed
in accordance with, the internal laws of the State of Colorado.

         13.   CONSTRUCTION. References in this Agreement to "this Agreement" 
and the words "herein," "hereof," "hereunder" and similar terms refer to this
Agreement, including all Exhibits, as a whole, unless the context otherwise
requires. The headings of the paragraphs of this Agreement have been included
for convenience of reference only, are not to be considered a part hereof and
shall not modify or restrict any of the terms or provisions hereof. All
decisions of the Company Board upon questions regarding this Agreement shall be
conclusive.


 
                                       10

<PAGE>   11



         14.   DUPLICATE ORIGINALS. The Company, TCI and Grantee may sign any
number of copies of this Agreement. Each signed copy shall be an original, but
all of them together represent the same agreement.

         15.   ENTIRE AGREEMENT. This Agreement is in satisfaction of and in 
lieu of all prior discussions and agreements, oral or written, between or among
TCI, the Company and Grantee, or any of them, with respect to the subject matter
hereof. Each of TCI, the Company and Grantee hereby declares and represents that
no promise or agreement not herein expressed has been made and that this
Agreement contains the entire agreement between and among the parties hereto
with respect to the SARs and supersedes and makes null and void any prior
agreements between or among TCI, the Company and Grantee, or any of them,
regarding the SARs.

         16.   AMENDMENT. This Agreement may be amended, modified or 
supplemented by the Company, without the consent of the Grantee, (i) to cure any
ambiguity or to correct or supplement any provision herein which may be
defective or inconsistent with any other provision herein or (ii) to make such
other changes as the Company, upon advice of counsel, determines are necessary
or advisable because of the adoption or promulgation of, or change in or of the
interpretation of, any law or governmental rule or regulation, including,
without limitation, any applicable federal or state securities laws. Except as
provided above, this Agreement may be amended, modified or supplemented only by
written agreement of the parties hereto.

         17.   DEFINITIONS. As used in this Agreement, the following terms have
the corresponding meanings:

               "AGREED PER SHARE VALUE" means the fair market value of a
share of Company Common Stock as of the Exercise Date, as agreed by Grantee and
the Company pursuant to paragraph 10(b) hereof.

               "APPLICABLE PERSON" means TCI or the Company, as applicable.

               "APPRAISER" means, as of any date of selection, an investment
banking firm of national reputation that is not affiliated with TCI, the Company
or Grantee.

               "APPROVED TRANSACTION", when used with respect to TCI or the
Company, as applicable, means any transaction in which the Relevant Board (or,
if approval of the Relevant Board is not required as a matter of law, the
stockholders of the Applicable Person) shall approve (i) any consolidation or
merger of the Applicable Person, or binding share exchange, pursuant to which
shares of common stock of the Applicable Person would be changed or converted
into or exchanged for cash, securities or other property, other than any such
transaction in which the common stockholders of the Applicable Person
immediately prior to such transaction have the same proportionate ownership of
the common stock of, and voting power with respect to, the surviving corporation
immediately after such transaction, (ii) any merger, consolidation or binding
share exchange to which the Applicable Person is a party as a result of which
the persons who are common

 
                                       11

<PAGE>   12



stockholders of the Applicable Person immediately prior thereto have less than a
majority of the combined voting power of the outstanding capital stock of the
Applicable Person ordinarily (and apart from the rights accruing under special
circumstances) having the right to vote in the election of directors immediately
following such merger, consolidation or binding share exchange, (iii) the
adoption of any plan or proposal for the liquidation or dissolution of the
Applicable Person, or (iv) any sale, lease, exchange or other transfer (in one
transaction or a series of related transactions) of all, or substantially all,
of the assets of the Applicable Person. Notwithstanding the foregoing, none of
such transactions that occur with respect to the Company while the Company is a
Subsidiary of TCI and that are effected in connection with a spin off of the
Company or rights offering of Company Common Stock to TCI's stockholders or
equivalent transaction shall constitute an Approved Transaction.

               "BOARD CHANGE" means, during any period of two consecutive
years, individuals who at the beginning of such period constituted the entire
Relevant Board cease for any reason to constitute a majority thereof unless the
election, or the nomination for election, of each new director was approved by a
vote of at least two-thirds of the directors then still in office who were
directors at the beginning of the period.

               "CAUSE" has the meaning ascribed thereto in any employment
agreement between Grantee and the applicable member of the TCI Group, and in the
absence of any such employment agreement shall include but not be limited to,
insubordination, dishonesty, incompetence, moral turpitude, other misconduct of
any kind or the refusal to perform one's duties and responsibilities for any
reason other than illness or incapacity, or negligence in the performance of any
of one's material duties or responsibilities that continues after written notice
from the Company, as determined in good faith by the Company Board; provided,
however, that if such termination occurs within twelve (12) months after (i) an
Approved Transaction, Control Purchase or Board Change occurs (x) with respect
to TCI following December 31, 1996 and prior to the earlier of such time as the
Company ceases to be a Subsidiary of TCI or such time as the Company becomes a
Public Company or (y) with respect to the Company at any time following December
31, 1996 that the Company is no longer a Subsidiary of TCI, or (ii) an Approved
Transaction occurs with respect to the Company at any time after December 31,
1996 and while the Company is a Subsidiary of TCI and after giving effect to
such Approved Transaction the Company will cease to be a Subsidiary of TCI, then
"Cause" shall mean only a felony conviction for fraud, misappropriation or
embezzlement.

               "CLOSING PRICE" of a share of any class or series of capital
stock on any day means the last sale price (or, if no last sale price is
reported, the average of the high bid and low asked prices) for a share of such
class or series of capital stock on such day (or, if such day is not a trading
day, on the next preceding trading day) as reported on NASDAQ or, if not
reported on NASDAQ, as quoted by the National Quotation Bureau Incorporated, or
if such class or series of capital stock is listed on an exchange, on the
principal exchange on which the shares are listed. If for any day the Closing
Price of a share of such class or series of capital stock is not determinable by
any of the foregoing means, then the Closing Price for such day shall be
determined in good faith by the

 
                                       12

<PAGE>   13



issuer's Board of Directors on the basis of such quotations and other
considerations as such Board deems appropriate

               "CODE" means the Internal Revenue Code of 1986, as amended from
time to time, or any successor statute or statutes thereto. Reference to any
specific Code section shall include any successor section.

               "COMPANY COMMON STOCK" means the Common Stock, $1.00 par value
per share, of the Company.

               "CONTROL PURCHASE" means any transaction (or series of related
transactions) in which (i) any person (as such term is defined in Sections
13(d)(3) and 14(d)(2) of the Exchange Act), corporation or other entity (other
than the Applicable Person, any Subsidiary of the Applicable Person or any
employee benefit plan sponsored by the Applicable Person or any Subsidiary of
the Applicable Person) shall purchase any common stock of the Applicable Person
(or securities convertible into common stock of the Applicable Person) for cash,
securities or any other consideration pursuant to a tender offer or exchange
offer, without the prior consent of the Relevant Board, or (ii) any person (as
such term is so defined), corporation or other entity (other than the Applicable
Person, any Subsidiary of the Applicable Person, any employee benefit plan
sponsored by the Applicable Person or any Subsidiary of the Applicable Person,
or any Controlling Person (as defined below)) shall become the "beneficial
owner" (as such term is defined in Rule 13d-3 under the Exchange Act), directly
or indirectly, of securities of the Applicable Person representing 20% or more
of the combined voting power of the then outstanding securities of the
Applicable Person ordinarily (and apart from the rights accruing under special
circumstances) having the right to vote in the election of directors (calculated
as provided in Rule 13d-3(d) under the Exchange Act in the case of rights to
acquire the Applicable Person's securities), other than in a transaction (or
series of related transactions) approved by the Relevant Board. For purposes of
this definition, "Controlling Person" means each of (a) the Chairman of the
Board, the President and each of the directors of the Applicable Person as of
December 31, 1996, (b) the respective family members, estates and heirs of (i)
Bob Magness and (ii) each of the persons referred to in clause (a) above, and
any trust or other investment vehicle for the primary benefit of any of such
persons or their respective family members or heirs and (c) Kearns-Tribune
Corporation, a Delaware corporation. As used with respect to any person, the
term "family member" means the spouse, siblings and lineal descendants of such
person.

               "DETERMINATION DATE" means February 1, 1996.

               "DISABILITY" means the inability to engage in any substantial
gainful activity by reason of any medically determinable physical or mental
impairment that (a) can be expected to result in death or (b) has lasted or can
be expected to last for a continuous period of not less than 12 months.


 
                                       13

<PAGE>   14



               "DOMESTIC RELATIONS ORDER" means a domestic relations order as
defined by the Code or Title I of the Employee Retirement Income Security Act of
1974, as amended, or the rules thereunder.

               "EXCHANGE ACT" means the Securities Exchange Act of 1934, as
amended from time to time, or any successor statute or statutes thereto, and the
rules and regulations promulgated by the Securities and Exchange Commission
thereunder. References to any specific section of the Exchange Act or rule
thereunder shall include any successor section or rule.

               "FAIR MARKET VALUE OF THE COMPANY" means the fair market value of
the Company as a going concern based upon the estimated market capitalization of
the Company as if it were a Public Company and the Company Common Stock were
publicly traded and widely held. In determining the Fair Market Value of the
Company, the Company and Grantee shall, and each Appraiser shall be instructed
to, value the assets held directly or indirectly by the Company in the following
manner (but without duplication): (i) with respect to any shares of capital
stock as to which there is a public trading market, at the Closing Price of such
shares on the Exercise Date, (ii) with respect to any shares of capital stock
which are not publicly traded, based on a widely distributed public trading
market value for such shares and as if such shares of capital stock were liquid
and freely tradeable on a major public trading market and (iii) with respect to
any assets of the Company which are not shares of capital stock, at the fair
market value thereof. In addition, the Company and Grantee shall, and such
Appraisers shall be instructed to, deduct from such value all indebtedness of
the Company (including preferred stock except to the extent such preferred stock
is deemed converted to Company Common Stock in connection with the calculation
of the Per Share Value); provided, however, that no such deduction shall be made
with respect to (i) the Company's obligations with respect to the Remaining SARs
held by Grantee and the Other SARs or (ii) any indebtedness of the Company
incurred in connection with the Company's satisfaction of its obligations with
respect to any prior exercise of SARs or Other SARs.

               "GOOD REASON" means the occurrence of any of the following prior
to any termination of employment by Grantee:

               (i) any reduction in Grantee's annual rate of salary (other than
         a reduction to which Grantee consents);

               (ii) a failure by TCI or the Company to continue in effect any
         employee benefit plan in which Grantee was participating, or the taking
         of any action by TCI or the Company that would adversely affect 
         Grantee's participation in, or materially reduce Grantee's benefits 
         under, any such employee benefit plan, unless such failure or such 
         taking of any action adversely affects the senior members of the 
         corporate management of TCI or the Company (as applicable) generally;


 
                                       14

<PAGE>   15



               (iii) the assignment to Grantee of duties and responsibilities
         that are materially more oppressive or onerous than those attendant to
         Grantee's position on the date hereof;

               (iv) the relocation of the office location as assigned to Grantee
         by the Company to a location more than 20 miles from Grantee's current
         location without Grantee's consent; or

               (v) the failure of the Company to obtain, prior to the time of
         any reorganization, merger, consolidation, disposition of all or
         substantially all of the assets of the Company or similar transaction
         effective after the date hereof, in which the Company is not the
         surviving person, the unconditional assumption in writing or by
         operation of law of the Company's obligations to Grantee under this
         Agreement by each direct successor to the Company in any such
         transaction.

               "NASDAQ" means the Nasdaq Stock Market.

               "OTHER SARS" means the stock appreciation rights relating to the
shares of Company Common Stock granted pursuant to certain Stock Appreciation
Right Agreements dated as of the date hereof among the Company, TCI and the
grantees named therein, respectively.

               "PER SHARE VALUE" means (x) if the Company is a Public Company as
of the Exercise Date, the Closing Price of a share of Company Common Stock as of
such date, and (y) if the Company is not a Public Company as of the Exercise
Date, the Agreed Per Share Value or the Appraised Per Share Value, as
applicable, of a share of Company Common Stock as of such date.

               "PUBLIC COMPANY" means a person the common equity securities of
which are registered under Section 12(b) or 12(g) of the Exchange Act and which
common equity securities are listed for trading on the New York Stock Exchange
or the NASDAQ National Market.

               "RELEVANT BOARD", when used with respect to TCI, means the Board
of Directors of TCI and, when used with respect to the Company, means the
Company Board.

               "STRIKE PRICE" means $32,911 per SAR, plus an interest factor of
6% per annum on such amount from the date hereof to the date of exercise
(calculated on the basis of a 365- day year and actual days elapsed), as such
amount per SAR may be adjusted from time to time pursuant to paragraph 9.

               "SUBSIDIARY", when used with respect to TCI or the Company, as
applicable, means any present or future subsidiary (as defined in Section 424(f)
of the Code) of the Applicable Person or any business entity in which the
Applicable Person owns, directly or indirectly, 50% or more of the voting,
capital or profits interests. An entity shall be deemed a Subsidiary of the
Applicable

 
                                       15

<PAGE>   16



Person for purposes of this definition only for such periods as the requisite
ownership or control relationship is maintained.

               "TCI GROUP" means TCI and its Subsidiaries, collectively, or the
applicable of TCI or a Subsidiary of TCI, as the context may require. If the
Company ceases to be a Subsidiary of TCI, the Company and its Subsidiaries
shall, notwithstanding the last sentence of the definition of Subsidiary above,
be deemed for purposes of this definition only to continue to be Subsidiaries of
TCI and, accordingly, members of the TCI Group.

         18.   RULES BY COMPANY BOARD. The rights of Grantee and obligations of
the Company hereunder shall be subject to such reasonable rules and regulations
as the Company Board may adopt from time to time hereafter.

 


                                      
                                     16

<PAGE>   17



               IN WITNESS WHEREOF, the Company, TCI and Grantee have caused this
Agreement to be duly executed and delivered as of the date first written above.



ATTEST:                                      TCI INTERNET SERVICES, INC.
                                           
                                           
                                           
                                             By:
-----------------------------                   --------------------------------
Assistant Secretary                             Name:
                                                Title:
                                           

                                             TELE-COMMUNICATIONS, INC.




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




                                             -----------------------------------
                                                           [Grantee]



 

<PAGE>   18


                                                          Exhibit A to Agreement
                                                    dated as of December 1, 1996



                           TCI INTERNET SERVICES, INC.

                            STOCK APPRECIATION RIGHT


                           DESIGNATION OF BENEFICIARY


         I, ____________________________________ (the "Grantee"), hereby declare

that upon my death ______________________________________ (the "Beneficiary") of
                                           Name
_______________________________________________________________________________,
Street Address                       City               State          Zip Code

who is my ____________________________________________, shall be entitled to the
                        Relationship to Grantee

stock appreciation rights and all other rights accorded Grantee by the
above-referenced grant agreement (the "Agreement").

         It is understood that this Designation of Beneficiary is made pursuant
to the Agreement and is subject to the conditions stated herein, including the
Beneficiary's survival of Grantee's death. If any such condition is not
satisfied, such rights shall devolve according to Grantee's will or the laws of
descent and distribution.

         All prior designations of beneficiary under the Agreement are hereby
revoked. This Designation of Beneficiary may only be revoked in writing, signed
by Grantee, and filed with TeleCommunications, Inc. and TCI Internet Services,
Inc., prior to Grantee's death.





-------------------------------                     ----------------------------
            Date                                       Grantee