<PAGE>

                                                                  EXHIBIT 10.33a


                               INKTOMI CORPORATION
                   SECOND AMENDMENT TO PARTICIPATION AGREEMENT

This SECOND AMENDMENT TO PARTICIPATION AGREEMENT (this "Amendment") dated as of
OCTOBER __, 2001, is by and among INKTOMI CORPORATION, a Delaware corporation,
as Lessee (the "Lessee"), WILMINGTON TRUST COMPANY, a Delaware banking
corporation, not in its individual capacity except as otherwise expressly
provided herein, but solely as Owner Trustee of the Inktomi Trust 2000 and
Lessor (the "Lessor"); WILMINGTON TRUST FSB, a federal savings bank, not in its
individual capacity except as otherwise expressly provided herein, but solely as
Co-Owner Trustee of the Inktomi Trust 2000 ("Co-Owner Trustee"); DEUTSCHE BANK
AG, NEW YORK BRANCH, a duly licensed branch of Deutsche Bank AG, a German
corporation, as an Investor (together with any permitted successors and assigns,
each an "Investor" and collectively the "Investors"); DEUTSCHE BANK AG, NEW YORK
AND/OR CAYMAN ISLANDS BRANCH, as a Lender (together with the other financial
institutions as may from time to time become lenders, the "Lenders") under the
Credit Agreement and as Agent for the Lenders (in such capacity, the "Agent");
and DEUTSCHE BANC ALEX. BROWN INC. f/k/a DEUTSCHE BANK SECURITIES, INC., as
Arranger (the "Arranger"). Capitalized terms used but not otherwise defined in
this Amendment shall have the meanings assigned to such terms in Annex A to the
Participation Agreement (as defined below).

                                    RECITALS:

        A. The Lessee, the Lessor, the Co-Owner Trustee, the Investors, the
Lenders, the Agent and the Arranger are parties to a certain Participation
Agreement, dated as of August 24, 2000 (as amended, restated, supplemented or
otherwise modified from time to time, the "Participation Agreement").

        B. The Lessee has requested a waiver of a provision of, and certain
amendments to, the Participation Agreement.

        C. The parties signatory hereto are willing to agree to the proposed
waiver and amendments on the terms, and subject to the conditions, hereinafter
set forth.

        NOW, THEREFORE, in consideration of the premises and the mutual
covenants hereinafter contained, the parties hereto agree as follows:

        1. Waiver. Section 9.5(h) of the Participation Agreement requires the
Lessee to maintain at the end of each fiscal quarter a Consolidated EBITDA of
not less than a designated amount. Subject to the satisfaction of the conditions
set forth in Section 5 below, the Participants agree to waive the requirement of
Section 9.5(h) for the fiscal quarter ending September 30, 2001.

<PAGE>

        2. Amendments to the Participation Agreement Subject to the satisfaction
of the conditions set forth in Section 6 below, the Participation Agreement is
hereby amended as follows:

              (a) Section 9.5(h) of the Participation Agreement is hereby
        amended by deleting the same in its entirety and replacing it with the
        following:

               "(h) Minimum Consolidated EBITDA. As at each date listed below,
               the Lessee shall not permit Consolidated EBITDA for the period
               referred to in the definition of such term ending on such date to
               be less than the amount set forth below opposite such date:

<TABLE>
<CAPTION>
DATE OF DETERMINATION           CONSOLIDATED EBITDA
---------------------           -------------------
<S>                             <C>
September 30, 2001                   waived
December 31, 2001                 ($8,000,000)
March 31, 2002                    ($8,000,000)
June 30, 2002                     ($3,000,000)
September 30, 2002                     $0
</TABLE>

               For each fiscal quarter thereafter the Lessee shall maintain a
               Consolidated EBITDA of not less than $0."

                (b) Section 9.5(k) to the Participation Agreement is hereby
        amended and restated as follows:

               "(k) Minimum Net Cash. The Lessee shall maintain as of the end of
               each fiscal quarter, commencing with the fiscal quarter ending on
               June 30, 2001, Minimum Net Cash in an amount of not less than
               $50,000,000 and commencing with the fiscal quarter ending March
               31, 2002, in an amount not less than the lesser of (i)
               $30,000,000 plus 50% of the net Cash proceeds to the Lessee from
               any equity offering consummated after October 19, 2001 and (ii)
               $50,000,000."

                (c) Section 9.5(f) to the Participation Agreement is hereby
        amended and restated as follows:

               "(f) Minimum Consolidated Tangible Net Worth. As of the end of
               each fiscal quarter, the Lessee's Consolidated Tangible Net Worth
               will not be less than $200,000,000 and commencing with the fiscal
               quarter ending December 31, 2001, the Lessee's Consolidated
               Tangible Net Worth will not be less than the lesser of (i)
               $125,000,000 plus 50% of the net Cash proceeds to the Lessee from
               any equity offering consummated after October 19, 2001 and (ii)
               $200,000,000."

                (d) Section 9.5(g) to the Participation Agreement is hereby
        amended and restated as follows:


                                       2
<PAGE>

               "(g) Minimum Consolidated Fixed Charge Ratio. The Lessee shall
               maintain as of the end of each fiscal quarter, from and after
               December 31, 2001, a minimum Consolidated Fixed Charge Ratio of
               at least 1.50 to 1.00."

                (e) Section 9.5(a) to the Participation Agreement is hereby
        amended as follows:

                        (i) paragraph (v) is amended by deleting the word "and"
                at the end thereof;

                        (ii) paragraph (vi) is amended by deleting the period at
                the end thereof and replacing it with "; and "; and

                        (iii) a new paragraph (vii) shall be added to read as
                follows:

                             "(vii) with each delivery of historical financial
               statements pursuant to paragraphs (i) or (ii) above, updated
               quarterly projected financial statements of the Lessee for each
               of the four fiscal quarters immediately following the date of the
               applicable historical financial statements being delivered
               pursuant to such paragraph, consisting of a balance sheet and
               statements of income and cash flows, and (2) proforma
               calculations for each such quarter demonstrating the Lessee's
               projected compliance with the financial covenants set forth in
               Sections 9.5 (f), (g), (h) and (k), substantially in the form set
               forth in Exhibit G to this Agreement."

        3. Amendments to Annex A. Subject to the satisfaction of the conditions
set forth in Section 6 below, Annex A to the Participation Agreement is hereby
amended as follows:

                (a) The definition of Cash Equivalents shall be amended and
        restated as follows:

        "'Cash Equivalents' means, as at any date of determination:

                             (1) Direct obligations of, or obligations the
                      principal and interest on which are unconditionally
                      guaranteed by, the United States of America or obligations
                      of any agency of the United States of America to the
                      extent such obligations are backed by the full faith and
                      credit of the United States of America, in each case
                      maturing within one year from the date of acquisition
                      thereof, certificates of deposit maturing within one year
                      from the date of acquisition thereof issued by a
                      commercial bank or trust company organized under the laws
                      of the United States of America or a state thereof or that
                      is a Participant, provided that (A) such deposits are
                      denominated in Dollars, (B) such bank or trust company has
                      capital, surplus and undivided profits of not less than
                      $1,000,000,000 and (C) such bank or trust company has
                      certificates of deposit or other debt obligations rated at
                      least A-1 (or its equivalent) by S&P or P-1 (or its
                      equivalent) by Moody's;


                                       3
<PAGE>

                             (2) Open market commercial paper maturing within
                      one year from the date of acquisition thereof issued by a
                      corporation organized under the laws of the United States
                      of America or a state thereof, provided such commercial
                      paper is rated at least A-1 (or its equivalent) by S&P or
                      P-1 (or its equivalent) by Moody's;

                             (3) Any repurchase agreement entered into with a
                      commercial bank or trust company organized under the laws
                      of the United States of America or a state thereof or that
                      is a Participant, provided that (A) such bank or trust
                      company has capital, surplus and undivided profits of not
                      less than $1,000,000,000, (B) such bank or trust company
                      has certificates of deposit or other debt obligations
                      rated at least A-1 (or its equivalent) by S&P or P-1 (or
                      its equivalent) by Moody's, (C) the repurchase obligations
                      of such bank or trust company under such repurchase
                      agreement are fully secured by a perfected security
                      interest in a security or instrument of the type described
                      in clause (1), (2) or (3) above and (D) such security or
                      instrument so securing the repurchase obligations has fair
                      market value at the time such repurchase agreement is
                      entered into of not less than 100% of such repurchase
                      obligations;

                             (4) Money Market fund shares of an institution
                      organized under the laws of the United States of America
                      or a state thereof or that is a Participant, provided that
                      (A) such institution has capital, surplus and undivided
                      profits of not less than $500,000,000, (B) the money
                      market fund of such institution is rated at least A-1 (or
                      its equivalent) by S&P or P-1 (or its equivalent) by
                      Moody's;

                             (5) Municipal notes, bonds, commercial paper,
                      municipal auction rate securities and municipal preferred
                      stock rated at least A-1 (or its equivalent) by S&P or P-1
                      (or its equivalent) by Moody's; provided, if any such item
                      matures more than one year from the date of determination
                      such item must be rated at least A+ (or its equivalent) by
                      S&P or A1 (or its equivalent) by Moody's; and

                             (6) Domestic, foreign and eurodollar corporate and
                      bank debt including, but not limited to, commercial paper,
                      corporate bonds, medium term notes, bankers' acceptances,
                      certificate of deposits, and taxable auction rate
                      securities rated at least A-1 (or its equivalent) by S&P
                      or P-1 (or its equivalent) by Moody's; provided, if any
                      such item matures more than one year from the date of
                      determination it must be rated at least A+ (or its
                      equivalent) by S&P or A1 (or its equivalent) by Moody's.

                                    For purposes of clauses (5) and (6), at any
                      date of determination not more than 5% of the total value
                      of all Cash Equivalents may be comprised of the securities
                      or obligations of any one issuer or obligor and its
                      affiliates, collectively. For purposes of Clause (1) -
                      (6),


                                       4
<PAGE>

                      not more than 15% of the total value of all Cash
                      Equivalents may have a maturity more than one year from
                      the date of determination."

                (b) The definition of Consolidated EBITDA shall be amended and
        restated as follows:

               "'Consolidated EBITDA' shall mean, for the Lessee and its
               Subsidiaries on a consolidated basis for any period, the sum of
               (i) Consolidated Net Income, plus (ii) Consolidated Interest
               Expense, plus (iii) Consolidated Income Tax Expense, plus (iv)
               Consolidated Depreciation and Amortization Expense, plus (v) one
               time professional fees and expenses associated with an
               acquisition, plus (vi) non cash charges associated with an
               acquisition for the write-down of good will associated with an
               acquisition, plus (vii) non cash charges associated with an
               acquisition for research and development costs of the acquired
               company expensed in the fiscal quarter of the acquisition, plus
               (viii) non cash charges related to deferred stock compensation
               expense, plus (ix) non-cash losses related to the Lessee's
               investments in equity securities, minus (x) non-cash gains
               related to the Lessee's investments in equity securities. For
               purposes of determining Consolidated EBITDA for the fiscal
               quarters ending December 31, 2001, March 31, 2002, June 30, 2002
               and September 30, 2002 each of the items utilized in the formula
               set forth in the previous sentence shall be based on the results
               of one fiscal quarter ending on such date of determination;
               provided that for purposes of determining Consolidated EBITDA,
               the Lessee and its Subsidiaries on a consolidated basis shall be
               permitted to exclude from such determination (i) non-recurring
               non-cash restructuring charges, and (ii) non-recurring cash
               restructuring charges not in excess of $7,000,000 for the fiscal
               quarter ending December 31, 2001 or $5,000,000 for any fiscal
               quarter ending thereafter. For purposes of determining
               Consolidated EBITDA as of any other date of determination, each
               of the items utilized in the formula set forth in the first
               sentence shall be based on the results of the two fiscal quarters
               ending on the date of determination."

                (c) The definition of Consolidated Fixed Charge Ratio shall be
        amended and restated as follows:

               "'Consolidated Fixed Charge Ratio' shall mean for the Lessee and
               its Subsidiaries on a consolidated basis at any date, the
               quotient of (a) the sum of (i) Consolidated EBITDA, plus (ii)
               Consolidated Lease Rental Expense, plus (iii) 100% of the net
               Cash proceeds to the Lessee from any equity offering received by
               the Lessee within twelve months prior to the date of
               determination, divided by (b) the sum of (i) CMLTD, plus (ii)
               Consolidated Interest Expense, plus (iii) Consolidated Lease
               Rental Expense. For purposes of determining the Consolidated
               Fixed Charge Ratio as of any date of determination (i) CMLTD will
               always be based upon the results of the most recent fiscal
               quarter, and (ii) each of the other items utilized in the formula
               set forth in the previous sentence shall be based on: for the
               fiscal quarter ending December 31, 2001, the results of such
               quarter; for the fiscal quarter ending March 31, 2002, the
               results of the two fiscal quarters ending on such date; for the
               fiscal quarter ending June 30, 2002, the results of the three


                                       5
<PAGE>
               fiscal quarters ending on such date; and for fiscal quarters
               ending September 30, 2002 and thereafter, the results of the four
               fiscal quarters ending on the date of determination."

        4. Amended Compliance Certificate. Subject to the satisfaction of the
conditions set forth in Section 5 below, Exhibit G to the Participation
Agreement shall be hereby amended and restated in the form set forth as Schedule
I to this Amendment.

        5. Representation and Warranties. The Lessee hereby represents and
warrants to the Lessor, the Co-Owner Trustee, the Investors, the Lenders, the
Agent and the Arranger that the following are true and correct on the date of
this Amendment and that, after giving effect to waiver and the amendments set
forth in Sections 1, 2, 3 and 4 above, the following will be true and correct on
the Effective Date (as defined below): The representations and warranties of the
Lessee as set forth in Section 7 of the Participation Agreement are true and
correct in all material respects as if made on such date (except for
representations and warranties expressly made as of a specified date, which
shall be true and correct in all material respects as of such date); No Default
or Event of Default has occurred and is continuing; and Each of the Operative
Agreements to which the Lessee is a party is in full force and effect.

        6. Effective Date. The waiver and amendments effected by Sections 1, 2,
3 and 4 above shall become effective as of the date of September 30, 2001 (the
"Effective Date"), subject to receipt by McGuireWoods LLP, counsel to the Agent
and the Arranger a copy of this Amendment duly executed by the Lessee, the
Co-Owner Trustee, the Investors, the Lenders, the Agent and the Arranger and
receipt by the Arranger of an amendment fee in the amount of $220,000.

        7. Miscellaneous.

                (a) Except as specifically waived above, the Participation
        Agreement and each of the Annex, Schedules and Exhibits thereto shall
        remain in full force and effect, and the Participation Agreement is
        hereby ratified and confirmed in all respects.

                (b) Section headings in this Agreement are included herein for
        convenience of reference only and shall not constitute a part of this
        Agreement for any other purpose.

                (c) This Agreement may be executed in any number of separate
        counterparts, each of which shall collectively and separately constitute
        one agreement. Delivery of an executed counterpart of a signature page
        to this Agreement by telecopier shall be effective as delivery of a
        manually executed counterpart of this Agreement.

        8. GOVERNING LAW. THIS AGREEMENT AND THE RIGHTS AND OBLIGATIONS OF THE
PARTIES HEREUNDER SHALL BE GOVERNED BY AND CONSTRUED, INTERPRETED AND ENFORCED
IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK.


                            [Signature pages follow]



                                       6
<PAGE>

        IN WITNESS WHEREOF, each party hereto has caused this Amendment to be
duly executed and delivered by its proper and duly authorized officer as of the
date first written above.

                                            INKTOMI CORPORATION,
                                            as Lessee

                                            By: /s/ Tim Stevens
                                               ---------------------------------
                                            Name:  Tim Stevens
                                            Title: Sr. VP of Business Affairs &
                                                   General Counsel


<PAGE>

                                            WILMINGTON TRUST COMPANY, not in its
                                            individual  capacity but solely as
                                            Owner Trustee and Lessor


                                            By: /s/ Anita Dallago
                                               ---------------------------------
                                            Name: Anita Dallago
                                            Title: Financial Services Officer


<PAGE>

                                            WILMINGTON TRUST FSB, not in its
                                            individual capacity but solely as
                                            Co-Owner Trustee



                                            By: /s/ Danald G. MacKalegg
                                               ---------------------------------
                                            Name:  Danald G. MacKalegg
                                            Title: Authorized Signer


<PAGE>


                                            DEUTSCHE BANK AG, NEW  YORK  BRANCH,
                                            as Investor

                                            By: /s/ David G. Dickinson, Jr.
                                               ---------------------------------
                                            Name:  David G. Dickinson, Jr.
                                            Title: Vice President



                                            By: /s/ John L. C. Ulrich
                                               ---------------------------------
                                            Name:  John L. C. Ulrich
                                            Title: Assistant Vice President


<PAGE>

                                            DEUTSCHE BANK AG, NEW YORK
                                            AND/OR CAYMAN ISLANDS BRANCH,
                                            as a Lender and as Agent for
                                            the Lenders

                                            By: /s/ David G. Dickinson, Jr.
                                               ---------------------------------
                                            Name:  David G. Dickinson, Jr.
                                            Title: Vice President


                                            By: /s/ John L. C. Ulrich
                                               ---------------------------------
                                            Name:   John L. C. Ulrich
                                            Title:  Assistant Vice President


<PAGE>

                                            DEUTSCHE BANC ALEX. BROWN INC.,
                                            f/k/a DEUTSCHE BANK SECURITIES,
                                            INC., as Arranger



                                            By: /s/ Robert F. Martorano, Jr.
                                               ---------------------------------
                                            Name:  Robert F. Martorano, Jr.
                                            Title: Managing Director


                                            By: /s/ Karen Keane
                                               ---------------------------------
                                            Name: Karen Keane
                                            Title:


<PAGE>


                                   SCHEDULE I

                                            EXHIBIT G TO PARTICIPATION AGREEMENT

                                     FORM OF

                             COMPLIANCE CERTIFICATE

        (i) I am the _____________ of Inktomi Corporation, a Delaware
corporation ("Lessee").

        (ii) I have reviewed the terms of that certain Participation Agreement,
dated as of August 24, 2000 (as amended, restated, supplemented or otherwise
modified from time to time, the "Participation Agreement"), among Inktomi
Corporation, a Delaware corporation, as lessee ("Lessee"), Wilmington Trust
Company, as Owner Trustee and Lessor, Wilmington Trust FSB, as Co-Owner Trustee,
Deutsche Bank AG, New York Branch, as an Investor, Deutsche Bank AG, New York
and/or Cayman Islands Branch, as Agent for the Lenders and as a Lender, and
Deutsche Bank Securities, Inc., as Arranger (capitalized terms used herein and
not otherwise defined herein shall have the meanings ascribed thereto in Annex A
to the Participation Agreement), and I have made, or have caused to be made
under my supervision, a review in reasonable detail of the transactions and
condition of Lessee and its Subsidiaries during the accounting period covered by
the financial statements delivered to you concurrently.

        (iii) The examination described in paragraph 2 above did not disclose,
and I have not knowledge of, the existence of any condition or event which
constitutes an Event of Default or Default during or at the end of the
accounting period covered by the attached financial statements or as of the date
of this Certificate, except as set forth in a separate attachment, if any, to
this Certificate, describing in detail, the nature of the condition or event,
the period during which it has existed and the action which Lessee has taken, is
taking, or proposes to take with respect to each such condition or event.

        The foregoing certifications, together with the computations set forth
in the Annex A hereto, are made and delivered this ___ day of _________,
________ pursuant to Section 9.5(a) of the Participation Agreement.


                                            INKTOMI CORPORATION


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

<PAGE>


                                   ANNEX A TO
                             COMPLIANCE CERTIFICATE

            FOR THE FISCAL QUARTER ENDING ________________, _________
                                  ($ in 000's)

<TABLE>
<CAPTION>
                                                                                    REQUIRED
                                                                   CALCULATION    RATIO/AMOUNT
                                                                   -----------    ------------
<S>     <C>                                                        <C>            <C>
1.      Consolidated Tangible Net Worth

        (i)    The Total Assets of the Lessee and its              $________
               Subsidiaries

        (ii)   The sum of:                                         $________
               (a)    the Total Liabilities of the Lessee and      $________
                      its Subsidiaries; and

               (b)    all Intangible Assets of Lessee and its      $________
                      Subsidiaries

        Consolidated Tangible Net Worth (i)-(ii)                   $________      $__________(1)

2.      Fixed Charge Ratio(2)

        (i)    The sum of:

               (a)    Consolidated EBITDA                          $________
               (b)    Consolidated Lease Rental Expense            $________
               (c)    Net Cash proceeds of equity issuance         $________
                      within prior 12 months

        (ii)   The sum of:

               (a)    CMLTD                                        $________
</TABLE>

--------

(1) Commencing with the fiscal quarter ending December 31, 2001, the required
    level is equal to the lesser of (i) $125,000,000 plus 50% of the net Cash
    proceeds of any equity offering received by the Lessee and (ii)
    $200,000,000.

(2) Applicable to reporting periods ending on or after December 31, 2001.


                                   Annex C-1
<PAGE>

<TABLE>
<CAPTION>
                                                                                    REQUIRED
                                                                   CALCULATION    RATIO/AMOUNT
                                                                   -----------    ------------
<S>     <C>                                                        <C>            <C>
               (b)    Consolidated Interest Expense                $________
               (c)    Consolidated Lease Rental Expense            $________

        The Ratio (i)/(ii)
                                                                   ___ to ___     1.5 to 1.0
3.      Consolidated EBITDA

        (i)    Consolidated Net Income                             $________

        (ii)   Consolidated Interest Expense                       $________

        (iii)  Consolidated Income Tax Expense                     $________

        (iv)   Consolidated Depreciation and Amortization Expense  $________

        (v)    Acquisition Professional Fees and Expenses          $________

        (vi)   Acquisition Non-Cash Charges (goodwill write-       $________
               down)

        (vii)  Acquisition Non-Cash Charges (research and          $________
               development costs of target)

        (viii) Non-Cash Deferred Compensation Charges              $________

        (ix)   Non-Cash Losses in the Lessee's investments in      $________
               equity securities

        (x)    Non-Cash Gains in the Lessee's investments in
               equity securities                                   $________

        (xi)   Non-Cash Non-recurring restructuring charges        $________

        (xii)  Non-recurring Cash restructuring charges            $________

               Consolidated EBITDA:
               (i)+(ii)+(iii)+(iv)+(v)+(vi)+(vii)+(viii)+(ix)-
               (x)+(xi)+(xii)
                                                                   $________      $________(3)
4.      Minimum Net Cash
</TABLE>

--------

(3) Consolidated EBITDA shall not be less than ($8,000,000) on December 31,
    2001, ($8,000,000) on March 31, 2002, ($3,000,000) on June 30, 2002, and $0
    on September 30, 2002. For any other date of determination, Consolidated
    EBITDA shall not be less than $0. The Lessee may not exclude the cash
    component of any restructuring charges in excess of $7,000,000 for the
    fiscal quarter ending on December 31, 2001 and $5,000,000 for each fiscal
    quarter thereafter through the fiscal quarter ending September 30, 2002.


                                   Annex C-2
<PAGE>

<TABLE>
<CAPTION>
                                                                                    REQUIRED
                                                                   CALCULATION    RATIO/AMOUNT
                                                                   -----------    ------------
<S>     <C>                                                        <C>            <C>
        (i)    Cash                                                $________
        (ii)   Cash Equivalents                                    $________
        (iii)  Total Cash and Cash Equivalents                     $________
        (iv)   Cash subject to any Lien (including the             $________
               Value of Qualified Securities)
        (v)    Total (iii)-(iv)                                    $________
        (vi)   Capitalized Lease Obligations                       $________
        (vii)  Contingent Obligations                              $________
        (viii) Principal amount of all Indebtedness                $________
        (ix)   Principal amount of all Off-Balance Sheet Debt      $________
               (other than the Off-Balance Sheet Debt under the
               Operative Agreements)
        (x)    Total ((vi) +(vii)+(viii)+(ix))                     $________

        Minimum Net Cash (v)-(x)                                   $________     $__________(4)
</TABLE>

--------

(4) Minimum Net Cash shall not be less than $50,000,000 and commencing with the
    fiscal quarter ending March 31, 2002 Minimum Net Cash shall not be less than
    the lesser of (i) $30,000,000 plus 50% of the net Cash proceeds to the
    Lessee from any equity offering and (ii) $50,000,000.


                                   Annex C-3