<PAGE>
 
                                                                    Exhibit 10.2


THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER
THE SECURITIES ACT OF 1933, AS AMENDED.  THE SECURITIES HAVE BEEN ACQUIRED FOR
INVESTMENT AND MAY NOT BE RESOLD, TRANSFERRED OR ASSIGNED IN THE ABSENCE OF AN
EFFECTIVE REGISTRATION STATEMENT FOR THE SECURITIES UNDER THE SECURITIES ACT OF
1933, AS AMENDED, OR AN OPINION OF COUNSEL THAT REGISTRATION IS NOT REQUIRED
UNDER SAID ACT.

                    Right to Purchase 124,756 Shares of Common Stock of OnHealth
                    Network Company



                           ONHEALTH NETWORK COMPANY

                                    FORM OF

                         COMMON STOCK PURCHASE WARRANT
NO. W-2

          ONHEALTH NETWORK COMPANY, a Washington corporation (the "Company"),
hereby certifies that, for value received, ADVANTAGE FUND II LTD. or registered
assigns (the "Holder"), is entitled, subject to the terms set forth below, to
purchase from the Company at any time or from time to time after the date
hereof, and before 5:00 p.m., New York City time, on the Expiration Date (as
hereinafter defined), 124,756 fully paid and nonassessable shares of Common
Stock at a purchase price per share equal to the Purchase Price (as hereinafter
defined).  The number of such shares of Common Stock and the Purchase Price are
subject to adjustment as provided in this Warrant.

          As used herein the following terms, unless the context otherwise
requires, have the following respective meanings:

          "Common Stock" includes the Company's Common Stock, $.01 par value per
     share, as authorized on the date hereof, and any other securities into
     which or for which the Common Stock may be converted or exchanged pursuant
     to a plan of recapitalization, reorganization, merger, sale of assets or
     otherwise.

          "Company" shall include OnHealth Network Company and any corporation
     that shall succeed to or assume the obligation of OnHealth Network Company
     hereunder in accordance 

                                      -1-
<PAGE>
 
     with the terms hereof.

          "Expiration Date" means October 30, 2003.

          "Issuance Date" shall mean the first date of original issuance of this
     Warrant.

          "Other Securities" refers to any stock (other than Common Stock) and
     other securities of the Company or any other person (corporate or
     otherwise) which the Holder at any time shall be entitled to receive, or
     shall have received, on the exercise of this Warrant, in lieu of or in
     addition to Common Stock, or which at any time shall be issuable or shall
     have been issued in exchange for or in replacement of Common Stock or Other
     Securities pursuant to Section 4.

          "Purchase Price" shall mean $4.809375 per share, subject to adjustment
     as provided in this Warrant.

          "Registration Rights Agreement" means the Registration Rights
     Agreement, dated as of October 30, 1998, by and between the Company and the
     original Holder of this Warrant, as amended from time to time in accordance
     with its terms.

          "Subscription Agreement" means the Subscription Agreement, dated as of
     October 30, 1998, by and between the Company and the original Holder of
     this Warrant, as amended from time to time in accordance with its terms.

          "Trading Day" means a day on which the principal securities market for
     the Common Stock is open for general trading of securities.

          1.   EXERCISE OF WARRANT.
               ------------------- 

          1.1  EXERCISE.  This Warrant may be exercised by the Holder hereof in
               --------                                                        
full or in part at any time or from time to time during the exercise period
specified in the first paragraph hereof until the Expiration Date by surrender
of this Warrant and the subscription form annexed hereto (duly executed by the
Holder), to the Company's transfer agent and registrar for the Common Stock, and
by making payment, in cash or by certified or official bank check payable to the
order of the Company, in the amount obtained by multiplying (a) the number of
shares of Common Stock designated by the Holder in the subscription form by (b)
the Purchase Price then in effect.  On any partial exercise the Company will
forthwith issue and deliver to or upon the order of the Holder hereof a new
Warrant or Warrants of like tenor, in the name of the Holder hereof or as the
Holder (upon payment by the Holder of any applicable transfer taxes) may
request, providing in the aggregate on the face or faces thereof for the
purchase of the number of shares of Common Stock for which such Warrant or
Warrants may still be exercised.

                                      -2-
<PAGE>
 
          1.2  NET ISSUANCE.  Notwithstanding anything to the contrary contained
               ------------                                                     
in Section 1.1, the Holder may elect to exercise this Warrant in whole or in
part by receiving shares of Common Stock equal to the net issuance value (as
determined below) of this Warrant, or any part hereof, upon surrender of this
Warrant to the Company's transfer agent and registrar for the Common Stock the
principal office of the Company together with the subscription form annexed
hereto (duly executed by the Holder), in which event the Company shall issue to
the Holder a number of shares of Common Stock computed using the following
formula:

          X = Y (A-B)
              -------
                 A

  Where:  X =  the number of shares of Common Stock to be issued to the
               Holder

               Y =  the number of shares of Common Stock as to which this
                    Warrant is to be exercised

               A =  the current fair market value of one share of Common Stock
                    calculated as of the last trading day immediately preceding
                    the exercise of this Warrant

               B =  the Purchase Price

          As used herein, current fair market value of Common Stock as of a
specified date shall mean with respect to each share of Common Stock the closing
sale price of the Common Stock on the principal securities market on which the
Common Stock may at the time be listed or, if there have been no sales on any
such exchange on such day, the average of the highest bid and lowest asked
prices on the principal securities market at the end of such day, or, if on such
day the Common Stock is not so listed, the average of the representative bid and
asked prices quoted in the Nasdaq System as of 4:00 p.m., New York City time,
or, if on such day the Common Stock is not quoted in the Nasdaq System, the
average of the highest bid and lowest asked price on such day in the domestic
over-the-counter market as reported by the National Quotation Bureau,
Incorporated, or any similar successor organization, in each such case averaged
over a period of five consecutive Trading Days consisting of the day as of which
the current fair market value of a share of Common Stock is being determined (or
if such day is not a Trading Day, the Trading Day next preceding such day) and
the four consecutive Trading Days prior to such day.  If on the date for which
current fair market value is to be determined the Common Stock is not listed on
any securities exchange or quoted in the Nasdaq System or the over-the-counter
market, the current fair market value of Common Stock shall be the highest price
per share which the Company could then obtain from a willing buyer (not a
current employee or director) for shares of Common Stock sold by the Company,
from authorized but unissued shares, as determined in good faith by the Board of

                                      -3-
<PAGE>
 
Directors of the Company, unless prior to such date the Company has become
subject to a merger, acquisition or other consolidation pursuant to which the
Company is not the surviving party, in which case the current fair market value
of the Common Stock shall be deemed to be the value received by the holders of
the Company's Common Stock for each share thereof pursuant to the Company's
acquisition.

          2.   DELIVERY OF STOCK CERTIFICATES, ETC., ON EXERCISE.  As soon as
               -------------------------------------------------             
practicable after the exercise of this Warrant, and in any event within three
Trading Days thereafter, the Company at its expense (including the payment by it
of any applicable issue or stamp taxes) will cause to be issued in the name of
and delivered to the Holder hereof, or as the Holder (upon payment by the Holder
of any applicable transfer taxes) may direct, a certificate or certificates for
the number of fully paid and nonassessable shares of Common Stock (or Other
Securities) to which the Holder shall be entitled on such exercise, in such
denominations as may be requested by the Holder, plus, in lieu of any fractional
share to which the Holder would otherwise be entitled, cash equal to such
fraction multiplied by the then current fair market value (as determined in
accordance with subsection 1.2) of one full share, together with any other stock
or other securities any property (including cash, where applicable) to which the
Holder is entitled upon such exercise pursuant to Section 1 or otherwise.  Upon
exercise of this Warrant as provided herein, the Company's obligation to issue
and deliver the certificates for Common Stock shall be absolute and
unconditional, irrespective of the absence of any action by the Holder to
enforce the same, any waiver or consent with respect to any provision thereof,
the recovery of any judgment against any person or any action to enforce the
same, any failure or delay in the enforcement of any other obligation of the
Company to the Holder, or any setoff, counterclaim, recoupment, limitation or
termination, or any breach or alleged breach by the Holder or any other person
of any obligation to the Company, and irrespective of any other circumstance
which might otherwise limit such obligation of the Company to the Holder in
connection with such exercise.  If the Company fails to issue and deliver the
certificates for the Common Stock to the Holder pursuant to the first sentence
of this paragraph as and when required to do so, in addition to any other
liabilities the Company may have hereunder and under applicable law, the Company
shall pay or reimburse the Holder on demand for all reasonable out-of-pocket
expenses including, without limitation, fees and expenses of legal counsel
incurred by the Holder as a result of such failure.

          3.   ADJUSTMENT FOR DIVIDENDS IN OTHER STOCK, PROPERTY, ETC.;
               --------------------------------------------------------
RECLASSIFICATION, ETC.  In case at any time or from time to time, all the
---------------------                                                    
holders of Common Stock (or Other Securities) shall have received, or (on or
after the record date fixed for the determination of shareholders eligible to
receive) shall have become entitled to receive, without payment therefor,

          (a) other or additional stock or other securities or property (other
     than cash) by way of dividend, or

                                      -4-
<PAGE>
 
          (b) any cash (excluding cash dividends payable solely out of earnings
     or earned surplus of the Company), or

          (c) other or additional stock or other securities or property
     (including cash) by way of spin-off, split-up, reclassification,
     recapitalization, combination of shares or similar corporate rearrangement,

other than additional shares of Common Stock (or Other Securities) issued as a
stock dividend or in a stock-split (adjustments in respect of which are provided
for in Section 5), then and in each such case the Holder, on the exercise hereof
as provided in Section 1, shall be entitled to receive the amount of stock and
other securities and property (including cash in the cases referred to in
subdivisions (b) and (c) of this Section 3) which the Holder would hold on the
date of such exercise if on the date thereof the Holder had been the holder of
record of the number of shares of Common Stock called for on the face of this
Warrant and had thereafter, during the period from the date hereof to and
including the date of such exercise, retained such shares and all such other or
additional stock and other securities and property (including cash in the case
referred to in subdivisions (b) and (c) of this Section 3) receivable by the
Holder as aforesaid during such period, giving effect to all adjustments called
for during such period by Section 4.

          4.   EXERCISE UPON REORGANIZATION, CONSOLIDATION, MERGER, ETC.  In
               --------------------------------------------------------     
case at any time or from time to time, the Company shall (a) effect a
reorganization, (b) consolidate with or merge into any other person, or (c)
transfer all or substantially all of its properties or assets to any other
person under any plan or arrangement contemplating the dissolution of the
Company, then, in each such case, as a condition of such reorganization,
consolidation, merger, sale or conveyance, the Company shall give at least 20
days notice to the Holder of such pending transaction whereby the Holder shall
have the right to exercise this Warrant prior to any such reorganization,
consolidation, merger, sale or conveyance.  Any exercise of this Warrant
pursuant to notice under this Section shall be conditioned upon the closing of
such reorganization, consolidation, merger, sale or conveyance which is the
subject of the notice and the exercise of this Warrant shall not be deemed to
have occurred until immediately prior to the closing of such transaction.

          5.   ADJUSTMENT FOR EXTRAORDINARY EVENTS.  In the event that the
               -----------------------------------                        
Company shall (i) issue additional shares of the Common Stock as a dividend or
other distribution on outstanding Common Stock, (ii) subdivide or reclassify its
outstanding shares of Common Stock, or (iii) combine its outstanding shares of
Common Stock into a smaller number of shares of Common Stock, then, in each such
event, the Purchase Price shall, simultaneously with the happening of such
event, be adjusted by multiplying the Purchase Price in effect immediately prior
to such event by a fraction, the numerator of which shall be the number of
shares of Common Stock outstanding immediately prior to such event and the
denominator of which shall be the number of shares of Common Stock outstanding
immediately after such event, and the product so obtained shall thereafter be
the 

                                      -5-
<PAGE>
 
Purchase Price then in effect. The Purchase Price, as so adjusted, shall be
readjusted in the same manner upon the happening of any successive event or
events described herein in this Section 5. The Holder shall thereafter, on the
exercise hereof as provided in Section 1, be entitled to receive that number of
shares of Common Stock determined by multiplying the number of shares of Common
Stock which would be issuable on such exercise immediately prior to such
issuance by a fraction of which (i) the numerator is the Purchase Price in
effect immediately prior to such issuance and (ii) the denominator is the
Purchase Price in effect on the date of such exercise.

          6.   FURTHER ASSURANCES.  The Company will take all action that may be
               ------------------                                               
necessary or appropriate in order that the Company may validly and legally issue
fully paid and nonassessable shares of stock, free from all taxes, liens and
charges with respect to the issue thereof, on the exercise of all or any portion
of this Warrant from time to time outstanding.

          7.   NOTICES OF RECORD DATE, ETC.  In the event of
               ---------------------------                  

          (a)  any taking by the Company of a record of the holders of any class
     of securities for the purpose of determining the holders thereof who are
     entitled to receive any dividend on, or any right to subscribe for,
     purchase or otherwise acquire any shares of stock of any class or any other
     securities or property, or to receive any other right, or

          (b)  any capital reorganization of the Company, any reclassification
     or recapitalization of the capital stock of the Company or any transfer of
     all or substantially all of the assets of the Company to or consolidation
     or merger of the Company with or into any other person, or

          (c)  any voluntary or involuntary dissolution, liquidation or winding-
     up of the Company,

then and in each such event the Company will mail or cause to be mailed to the
Holder, at least ten days prior to such record date, a notice specifying (i) the
date on which any such record is to be taken for the purpose of such dividend,
distribution or right, and stating the amount and character of such dividend,
distribution or right, (ii) the date on which any such reorganization,
reclassification, recapitalization, transfer, consolidation, merger,
dissolution, liquidation or winding-up is to take place, and the time, if any is
to be fixed, as of which the holders of record of Common Stock (or Other
Securities) shall be entitled to exchange their shares of Common Stock (or Other
Securities) for securities or other property deliverable on such reorganization,
reclassification, recapitalization, transfer, consolidation, merger,
dissolution, liquidation or winding-up, and (iii) the amount and character of
any stock or other securities, or rights or options with respect thereto,
proposed to be issued or granted, the date of such proposed issue or grant and
the persons or class of persons to whom such proposed issue or grant is to be
offered or made.  Such notice shall also state that the 

                                      -6-
<PAGE>
 
action in question or the record date is subject to the effectiveness of a
registration statement under the Securities Act of 1933, as amended (the
"Securities Act"), or a favorable vote of shareholders if either is required.
Such notice shall be mailed at least ten days prior to the date specified in
such notice on which any such action is to be taken or the record date,
whichever is earlier.

          8.   RESERVATION OF STOCK, ETC., ISSUABLE ON EXERCISE OF WARRANTS.
               ------------------------------------------------------------  
The Company will at all times reserve and keep available out of its authorized
but unissued shares of capital stock, solely for issuance and delivery on the
exercise of this Warrant, a sufficient number of shares of Common Stock (or
Other Securities) to effect the full exercise of this Warrant and the exercise,
conversion or exchange of any other warrant or security of the Company
exercisable for, convertible into, exchangeable for or otherwise entitling the
holder to acquire shares of Common Stock (or Other Securities), and if at any
time the number of authorized but unissued shares of Common Stock (or Other
Securities) shall not be sufficient to effect such exercise, conversion or
exchange, the Company shall take such action as may be necessary to increase its
authorized but unissued shares of Common Stock (or Other Securities) to such
number as shall be sufficient for such purposes.

          9.   TRANSFER OF WARRANT.  This Warrant shall inure to the benefit of
               -------------------                                             
the successors to and assigns of the Holder.  This Warrant and all rights
hereunder, in whole or in part, are registrable at the office or agency of the
Company referred to below by the Holder hereof in person or by his duly
authorized attorney, upon surrender of this Warrant properly endorsed.

          10.  REGISTER OF WARRANTS.  The Company shall maintain, at the
               --------------------                                     
principal office of the Company (or such other office as it may designate by
notice to the Holder hereof), a register in which the Company shall record the
name and address of the person in whose name this Warrant has been issued, as
well as the name and address of each successor and prior owner of such Warrant.
The Company shall be entitled to treat the person in whose name this Warrant is
so registered as the sole and absolute owner of this Warrant for all purposes.

          11.  EXCHANGE OF WARRANT.  This Warrant is exchangeable, upon the
               -------------------                                         
surrender hereof by the Holder hereof at the office or agency of the Company
referred to in Section 10, for one or more new Warrants of like tenor
representing in the aggregate the right to subscribe for and purchase the number
of shares of Common Stock which may be subscribed for and purchased hereunder,
each of such new Warrants to represent the right to subscribe for and purchase
such number of shares as shall be designated by said Holder hereof at the time
of such surrender.

          12.  REPLACEMENT OF WARRANT.  On receipt of evidence reasonably
               ----------------------                                    
satisfactory to the Company of the loss, theft, destruction or mutilation of
this Warrant and, in the case of any such loss, theft or destruction of this
Warrant, on delivery of an indemnity agreement or security reasonably
satisfactory in form and amount to the Company or, in the case of any such
mutilation, 

                                      -7-
<PAGE>
 
on surrender and cancellation of this Warrant, the Company at its expense will
execute and deliver, in lieu thereof, a new Warrant of like tenor.

          13.  WARRANT AGENT.  On or prior to the issuance of this Warrant, the
               -------------                                                   
Company will instruct American Stock Transfer & Trust Company, as Transfer Agent
and Registrar (the "Transfer Agent"), to act as the exercise agent for purposes
of issuing shares of Common Stock (or Other Securities) on the exercise of this
Warrant pursuant to Section 1, exchanging this Warrant pursuant to Section 11
and replacing this Warrant pursuant to Section 12, or any of the foregoing, and
thereafter any such exchange or replacement, as the case may be, shall be made
at such office by such agent.

          14.  REMEDIES.  The Company stipulates that the remedies at law of the
               --------                                                         
Holder in the event of any default or threatened default by the Company in the
performance of or compliance with any of the terms of this Warrant are not and
will not be adequate, and that such terms may be specifically enforced by a
decree for the specific performance of any agreement contained herein or by an
injunction against a violation of any of the terms hereof or otherwise.

          15.  NO RIGHTS OR LIABILITIES AS A SHAREHOLDER.  This Warrant shall
               -----------------------------------------                     
not entitle the Holder hereof to any voting rights or other rights as a
shareholder of the Company.  No provision of this Warrant, in the absence of
affirmative action by the Holder hereof to purchase Common Stock, and no mere
enumeration herein of the rights or privileges of the Holder hereof, shall give
rise to any liability of the Holder for the Purchase Price or as a shareholder
of the Company, whether such liability is asserted by the Company or by
creditors of the Company.

          16.  NOTICES, ETC.  All notices and other communications from the
               ------------                                                
Company to the registered Holder shall be mailed by first class certified mail,
postage prepaid, at such address as may have been furnished to the Company in
writing by the Holder or at the address shown for the Holder on the register of
Warrants referred to in Section 10.

          17.  TRANSFER RESTRICTIONS.  By acceptance of this Warrant, the Holder
               ---------------------                                            
represents to the Company that this Warrant is being acquired for the Holder's
own account and for the purpose of investment and not with a view to, or for
sale in connection with, the distribution thereof, nor with any present
intention of distributing or selling the Warrant or the Common Stock issuable
upon exercise of the Warrant.  The Holder acknowledges and agrees that this
Warrant and, except as otherwise provided in the Registration Rights Agreement,
the shares of Common Stock issuable upon exercise of this Warrant (if any) have
not been (and at the time of acquisition by the Holder, will not have been or
will not be), registered under the Securities Act or under the securities laws
of any state, in reliance upon certain exemptive provisions of such statutes.
The Holder further recognizes and acknowledges that because this Warrant and,
except as provided in the Registration Rights Agreement, the shares of Common
Stock issuable upon exercise of this Warrant (if any) are 

                                      -8-
<PAGE>
 
unregistered, they may not be eligible for resale, and may only be resold in the
future pursuant to an effective registration statement under the Securities Act
and any applicable state securities laws, or pursuant to a valid exemption from
such registration requirements. Unless the shares of Common Stock issuable upon
exercise of this Warrant have theretofore been registered for resale under the
Securities Act, the Company may require, as a condition to the issuance of
Common Stock upon the exercise of this Warrant (i) in the case of an exercise in
accordance with Section 1.1 hereof, a confirmation as of the date of exercise of
the Holder's representations pursuant to this Section 17, or (ii) in the case of
an exercise in accordance with Section 1.2 hereof, an opinion of counsel
reasonably satisfactory to the Company that the shares of Common Stock to be
issued upon such exercise may be issued without registration under the
Securities Act.

          18.  LEGEND.  Unless theretofore registered for resale under the
               ------                                                     
Securities Act, each certificate for shares issued upon exercise of this Warrant
shall bear the following legend:

     The securities represented by this certificate have not been registered
     under the Securities Act of 1933, as amended.  The securities have been
     acquired for investment and may not be resold, transferred or assigned in
     the absence of an effective registration statement for the securities under
     the Securities Act of 1933, as amended, or an opinion of counsel that
     registration is not required under said Act.

          19.  MISCELLANEOUS.  This Warrant and any terms hereof may be changed,
               -------------                                                    
waived, discharged or terminated only by an instrument in writing signed by the
party against which enforcement of such change, waiver, discharge or termination
is sought.  This Warrant shall be construed and enforced in accordance with and
governed by the internal laws of the State of Washington.  The headings in this
Warrant are for purposes of reference only, and shall not limit or otherwise
affect any of the terms hereof.  The invalidity or unenforceability of any
provision hereof shall in no way affect the validity or enforceability of any
other provision.

                                      -9-
<PAGE>
 
          IN WITNESS WHEREOF, the Company has caused this Warrant to be executed
on its behalf by one of its officers thereunto duly authorized.

Dated:  October 30, 1998              ONHEALTH NETWORK COMPANY



                                      By:  \s\ Michael D. Conway
    
                                      Title:   Vice President

                                      -10-
<PAGE>
 
                             FORM OF SUBSCRIPTION

                           ONHEALTH NETWORK COMPANY

                  (To be signed only on exercise of Warrant)

TO:  American Stock Transfer & Trust Company,
      as Exercise Agent
     6201 Fifteenth Avenue
     Brooklyn, New York 11219

     1.   The undersigned Holder of the attached original, executed Warrant
hereby elects to exercise its purchase right under such Warrant with respect to
______________ shares of Common Stock, as defined in the Warrant, of OnHealth
Network Company, a Washington corporation (the "Company").

     2.   The undersigned Holder (check one):

[_]  (a)  elects to pay the aggregate purchase price for such shares of Common
          Stock (the "Exercise Shares") (i) by lawful money of the United States
          or the enclosed certified or official bank check payable in United
          States dollars to the order of the Company in the amount of
          $___________, or (ii) by wire transfer of United States funds to the
          account of the Company in the amount of $____________, which transfer
          has been made before or simultaneously with the delivery of this Form
          of Subscription pursuant to the instructions of the Company;

or

[_]  (b)  elects to receive shares of Common Stock having a value equal to the
          value of the Warrant calculated in accordance with Section 1.2 of the
          Warrant.

     3.   Please issue a stock certificate or certificates representing the
appropriate number of shares of Common Stock in the name of the undersigned or
in such other names as is specified below:

     Name:

     Address:

                                      -11-
<PAGE>
 
Dated:_______________________                 (Signature must conform to name of
                                              Holder as specified on the face of
                                              Warrant)


                                        Name:

                                        Address:

                                      -12-