<PAGE>
                                                                   EXHIBIT 10.36


                                 PROMISSORY NOTE

                                   $2,000,000

                             FOSTER CITY, CALIFORNIA
                                DECEMBER 10, 2001

        WHEREAS, it is the intention of Inktomi Corporation to encourage and
provide its Chief Executive Officer with an incentive to retain his investments
in its stock and to focus on growing the company. Under the current environment,
by extending credit to its Chief Executive Officer, Inktomi Corporation can
limit any negative inferences or impact to the company that may arise from its
Chief Executive Officer's sale of a significant amount of its stock to meet his
short-term cash needs due to factors beyond his individual control including his
personal lock-up on sale of stock for an extended period of time. This paragraph
is not intended to create any binding obligation.

        FOR VALUE RECEIVED, David C. Peterschmidt (the "Borrower"), hereby
promises to pay to the order of Inktomi Corporation, a Delaware corporation (or
its successor upon any sale, merger, acquisition or reorganization) (the
"Lender"), the principal sum of Two Million Dollars ($2,000,000), in lawful
money of the United States of America, on December 10, 2003 or when earlier
required pursuant to Sections 7, 8, 9 or 10 hereof (the "Repayment Date").

        1. Interest Rate. The outstanding principal amount of this Note,
together with all accrued and unpaid interest thereon, shall bear interest at a
rate per annum equal to prime at the time of issuance plus one (6%).

        2. Interest Payments. Interest payments on the Note shall be payable in
cash on the Repayment Date. Interest shall be calculated on the basis of a year
comprised of twelve (12) thirty (30) day months.

        3. No Usury. This Note is hereby expressly limited so that in no event
whatsoever, whether by reason of deferment or advancement of loan proceeds,
acceleration of maturity of the loan evidenced hereby, or otherwise, shall the
amount paid or agreed to be paid to the Lender hereunder for the loan, use,
forbearance or detention of money exceed the maximum interest rate permitted by
the laws of the State of California. If at any time the performance of any
provision involves a payment exceeding the limit of the price that may be
validly charged for the loan, use, forbearance or detention of money under
applicable law, then automatically and retroactively, ipso facto, the obligation
to be performed shall be reduced to such limit, it being the specific intent of
the Company and the Borrower that all payments under this Note are to be
credited first to interest as permitted by law, but not in excess of (i) the
agreed rate of interest hereunder, or (ii) that permitted by law, whichever is
the lesser, and the balance toward the reduction of principal.

        4. Method of Payment. All payments hereunder shall be made by cash or
check to Lender, Inktomi Corporation, 4100 East 3rd Avenue, Foster City, CA
94404, or at such other place, or by such other means, as the Lender shall
designate to the Borrower in writing. If any payment of principal or interest on
this Note is due on a day which is not a Business Day,

<PAGE>
such payment shall be due on the next succeeding Business Day. "Business Day"
means any day other than a Saturday, Sunday or legal holiday in the State of
California.

        5. Prepayment. The Borrower shall have the right to prepay the principal
amount hereof in full or in part, together with all accrued interest on the
amount prepaid to the date of such prepayment, at any time without penalty.

        6. Reserved.

        7. Events of Default.

           (a) The occurrence of one or more of the following shall constitute
an event of default ("Event of Default") hereunder:

               (i) The Borrower's failure to pay any payment of principal or
interest on the Note when due;

               (ii) If, pursuant to or within the meaning of the United States
Bankruptcy Code or any other federal or state law relating to insolvency or
relief of debtors ("Bankruptcy Law"), the Borrower shall (a) commence a
voluntary case or proceeding, (b) consent to the entry of an order for relief
against the Borrower, in an involuntary case, (c) consent to the appointment of
a trustee, receiver, assignee, liquidator or similar official, (d) make an
assignment for the benefit of the Borrower's creditors, or (e) admit in writing
the Borrower's inability to pay Borrower's debts as they become due;

               (iii) If a court of competent jurisdiction enters an order or
decree under any Bankruptcy Law that (a) is for relief against the Borrower in
an involuntary case, (b) appoints a trustee, receiver, assignee, liquidator or
similar official for the Borrower or substantially all of the Borrower's
properties, (c) orders the liquidation of the Borrower, and in each case the
order or decree is not dismissed within 30 days; or

               (iv) The occurrence of an event described in Section 8 hereof, or
the Borrower's failure to observe or perform any covenant or agreement contained
in this Note including, but not limited to, Sections 9 and 10 hereof;

           (b) Upon the occurrence of an Event of Default, the principal of this
Note, together with all unpaid interest and all other amounts payable hereunder,
shall become due and payable forthwith, without presentment, demand, notice,
protest or other requirement of any kind, all of which are expressly waived by
Borrower. Upon the occurrence of an Event of Default (unless all Events of
Default have been cured or waived by Lender), Lender may, at its option, by
written notice of Borrower, declare the entire unpaid principal balance of this
Note, together with all accrued interest thereon, immediately due and payable
regardless of any prior forbearance. In either such case, Lender may exercise
any and all rights and remedies available to it under applicable law, including,
without limitation, the right to collect from Borrower all sums due under this
Note. Borrower shall pay all reasonable costs and expenses of collection
incurred by or on behalf of Lender as a result of an Event of Default including,
without limitation, reasonable attorneys' fees.


                                       2
<PAGE>
        8. Termination of Employment. Upon the termination of the Borrower's
employment with the Lender for any reason, including, without limitation, with
or without cause, or by reason of death or disability, the entire unpaid
principal balance plus all accrued and unpaid interest of this Note, and any
other charges owing to the Lender, shall become due and payable one hundred and
twenty (120) days after the date of such termination of such employment,
irrespective of the maturity date of this Note. Nothing in this Note shall
create any employment right or entitlement in favor of the Borrower, which
employment with the Lender shall remain "at-will."

        9. Mandatory Prepayment on Receipt of Bonus. If at any time, or from
time to time, Borrower shall receive any compensatory bonus from the Company
(including, but not limited to, cash payments, cash dividends or other
distributions), but not including payments or distributions in the form of
Lender capital stock, then the after-tax proceeds (the "Net Proceeds") from such
compensatory bonus shall be applied to the prepayment of the unpaid principal
balance plus all accrued and unpaid interest of this Note within seven (7)
calendar days after receipt thereof (the "Mandatory Prepayment Period"). If the
Lender does not receive such Net Proceeds within the Mandatory Prepayment
Period, the entire principal balance plus all accrued and unpaid interest of
this Note shall become immediately due and payable pursuant to Section 7 hereof.

        10. Mandatory Prepayment on Sale of Stock. If at any time, or from time
to time, Borrower shall receive any proceeds from the sale or other disposition
of shares of Lender capital stock now owned or hereinafter acquired by Borrower
("Borrower Stock"), then 50% of the after-tax proceeds (the "Borrower Stock
Proceeds") of such sale or other disposition shall be applied to the prepayment
of the unpaid principal balance plus all accrued and unpaid interest of this
Note within the Mandatory Prepayment Period. If the Lender does not receive such
Borrower Stock Proceeds within the Mandatory Prepayment Period, the entire
principal balance plus all accrued and unpaid interest of this Note shall become
immediately due and payable pursuant to Section 7 hereof.

        11. Recourse. The Lender shall be entitled to recourse against the
Borrower for the payment of any principal and accrued interest of the Note or
for any claim based hereon (including costs of collection).

        12. Costs of Collection. Upon the failure of the Borrower to pay any
amount due hereunder as and when due, the Borrower shall pay on demand any
reasonable costs and expenses incurred by the holder hereof in connection with
the collection of any outstanding principal and in connection with the
enforcement of any rights or remedies provided for pursuant to this Note. If not
paid on demand, all such costs and expenses automatically shall be added to the
remaining principal balance hereunder as of the date immediately following the
date of such demand.

        13. Waiver. The Borrower hereby waives any right it might otherwise have
to require notice or acceptance by any other person of its obligations or
liabilities under this Note which are unconditional and absolute and waives
diligence, presentment, demand of payment, protest and notice with respect to
all of the obligations of the Borrower under this Note and with respect to any
action under this Note and all other notices and demands whatsoever, except as


                                       3
<PAGE>
specifically provided for in this Note. This Note may be amended, and the
observance of any term of this Note may be waived, with (and only with) the
written consent of the Lender.

        14. Governing Law. This Note shall be governed by and construed in
accordance with the laws of the State of California.

        15. Assignment or Pledge of Note. The Lender shall promptly notify the
Borrower of any endorsement, assignment, pledge or hypothecation of this Note to
a person not affiliated with the Lender. This Note may not be sold, assigned,
hypothecated, delegated or transferred by the Borrower, by operation of law or
otherwise, without prior written consent of the Lender.

        16. Loss, Mutilation, Etc. Upon notice from the holder of this Note to
the Borrower of the loss, theft, destruction or mutilation of this Note, and
upon receipt of an indemnity reasonably satisfactory to the Borrower from the
holder of this Note or, in the case of mutilation hereof, upon surrender of the
mutilated Note, the Borrower will make and deliver a new note of like tenor in
lieu of this Note.

        17. Notices. All notices and other communications required or permitted
under this Note shall be in writing and shall be personally delivered or sent by
certified first class United States mail, postage prepaid, return receipt
requested, and if mailed, shall be deemed to have been received on the third
business day after deposit in the mail, addressed to the Lender, Inktomi
Corporation, 4100 East 3rd Avenue, Foster City, California 94404, Attention:
General Counsel, or to the Borrower at the address set forth below the
Borrower's signature. Notice of any change of either party's address shall be
given by written notice in the manner set forth in this paragraph.

        18. Severability. If any provision in this Note is construed to be
invalid, illegal or unenforceable, then the remaining provisions shall not in
any way be affected thereby and shall be enforced without regard thereto.


                                       4
<PAGE>
        IN WITNESS WHEREOF, the Borrower has executed this Note on the date
first above written.

                                       BORROWER:

                                       /s/ David C. Peterschmidt
                                       -----------------------------------------
                                       Signature of Borrower

                                       -----------------------------------------
                                       Print or Type Name: David C. Peterschmidt

                                       -----------------------------------------
                                       Address

                                       -----------------------------------------
                                       City, State, Zip Code

                                       -----------------------------------------
                                       Telephone Number


AGREED AND ACCEPTED

/s/ Jerry Kennelly
-----------------------------------
Title: Chief Financial Officer

Inktomi Corporation
4100 East 3rd Avenue
Foster City, CA 94404

<PAGE>
           THIS NOTE WAS PAID IN FULL BY BORROWER ON DECEMBER 21, 2001

                                 PROMISSORY NOTE

                                  $2,663,134.48

                             FOSTER CITY, CALIFORNIA
                                DECEMBER 18, 2001

        WHEREAS, it is the intention of Inktomi Corporation to encourage and
provide its Chief Executive Officer with an incentive to retain his investments
in its stock and to focus on growing the company. Under the current environment,
by extending credit to its Chief Executive Officer, Inktomi Corporation can
limit any negative inferences or impact to the company that may arise from its
Chief Executive Officer's sale of a significant amount of its stock to meet his
short-term cash needs due to factors beyond his individual control including his
personal lock-up on sale of stock for an extended period of time. This paragraph
is not intended to create any binding obligation.

        FOR VALUE RECEIVED, David C. Peterschmidt (the "Borrower"), hereby
promises to pay to the order of Inktomi Corporation, a Delaware corporation (or
its successor upon any sale, merger, acquisition or reorganization) (the
"Lender"), the principal sum of Two Million Six Hundred Sixty Three Thousand One
Hundred Thirty Four Dollars and Forty-Eight Cents ($2,663,134.48), in lawful
money of the United States of America, on December 18, 2003 or when earlier
required pursuant to Sections 7, 8, 9 or 10 hereof (the "Repayment Date").

        1. Interest Rate. The outstanding principal amount of this Note,
together with all accrued and unpaid interest thereon, shall bear interest at a
rate per annum equal to prime at the time of issuance plus one (6%).

        2. Interest Payments. Interest payments on the Note shall be payable in
cash on the Repayment Date. Interest shall be calculated on the basis of a year
comprised of twelve (12) thirty (30) day months.

        3. No Usury. This Note is hereby expressly limited so that in no event
whatsoever, whether by reason of deferment or advancement of loan proceeds,
acceleration of maturity of the loan evidenced hereby, or otherwise, shall the
amount paid or agreed to be paid to the Lender hereunder for the loan, use,
forbearance or detention of money exceed the maximum interest rate permitted by
the laws of the State of California. If at any time the performance of any
provision involves a payment exceeding the limit of the price that may be
validly charged for the loan, use, forbearance or detention of money under
applicable law, then automatically and retroactively, ipso facto, the obligation
to be performed shall be reduced to such limit, it being the specific intent of
the Company and the Borrower that all payments under this Note are to be
credited first to interest as permitted by law, but not in excess of (i) the
agreed rate of interest hereunder, or (ii) that permitted by law, whichever is
the lesser, and the balance toward the reduction of principal.

<PAGE>
        4. Method of Payment. All payments hereunder shall be made by cash or
check to Lender, Inktomi Corporation, 4100 East 3rd Avenue, Foster City, CA
94404, or at such other place, or by such other means, as the Lender shall
designate to the Borrower in writing. If any payment of principal or interest on
this Note is due on a day which is not a Business Day, such payment shall be due
on the next succeeding Business Day. "Business Day" means any day other than a
Saturday, Sunday or legal holiday in the State of California.

        5. Prepayment. The Borrower shall have the right to prepay the principal
amount hereof in full or in part, together with all accrued interest on the
amount prepaid to the date of such prepayment, at any time without penalty.

        6. Reserved.

        7. Events of Default.

           (a) The occurrence of one or more of the following shall constitute
an event of default ("Event of Default") hereunder:

               (i) The Borrower's failure to pay any payment of principal or
interest on the Note when due;

               (ii) If, pursuant to or within the meaning of the United States
Bankruptcy Code or any other federal or state law relating to insolvency or
relief of debtors ("Bankruptcy Law"), the Borrower shall (a) commence a
voluntary case or proceeding, (b) consent to the entry of an order for relief
against the Borrower, in an involuntary case, (c) consent to the appointment of
a trustee, receiver, assignee, liquidator or similar official, (d) make an
assignment for the benefit of the Borrower's creditors, or (e) admit in writing
the Borrower's inability to pay Borrower's debts as they become due;

               (iii) If a court of competent jurisdiction enters an order or
decree under any Bankruptcy Law that (a) is for relief against the Borrower in
an involuntary case, (b) appoints a trustee, receiver, assignee, liquidator or
similar official for the Borrower or substantially all of the Borrower's
properties, (c) orders the liquidation of the Borrower, and in each case the
order or decree is not dismissed within 30 days; or

               (iv) The occurrence of an event described in Section 8 hereof, or
the Borrower's failure to observe or perform any covenant or agreement contained
in this Note including, but not limited to, Sections 9 and 10 hereof;

           (b) Upon the occurrence of an Event of Default, the principal of this
Note, together with all unpaid interest and all other amounts payable hereunder,
shall become due and payable forthwith, without presentment, demand, notice,
protest or other requirement of any kind, all of which are expressly waived by
Borrower. Upon the occurrence of an Event of Default (unless all Events of
Default have been cured or waived by Lender), Lender may, at its option, by
written notice of Borrower, declare the entire unpaid principal balance of this
Note, together with all accrued interest thereon, immediately due and payable
regardless of any prior forbearance. In either such case, Lender may exercise
any and all rights and remedies available

<PAGE>
to it under applicable law, including, without limitation, the right to collect
from Borrower all sums due under this Note. Borrower shall pay all reasonable
costs and expenses of collection incurred by or on behalf of Lender as a result
of an Event of Default including, without limitation, reasonable attorneys'
fees.

        8. Termination of Employment. Upon the termination of the Borrower's
employment with the Lender for any reason, including, without limitation, with
or without cause, or by reason of death or disability, the entire unpaid
principal balance plus all accrued and unpaid interest of this Note, and any
other charges owing to the Lender, shall become due and payable one hundred and
twenty (120) days after the date of such termination of such employment,
irrespective of the maturity date of this Note. Nothing in this Note shall
create any employment right or entitlement in favor of the Borrower, which
employment with the Lender shall remain "at-will."

        9. Mandatory Prepayment on Receipt of Bonus. If at any time, or from
time to time, Borrower shall receive any compensatory bonus from the Company
(including, but not limited to, cash payments, cash dividends or other
distributions), but not including payments or distributions in the form of
Lender capital stock, then the after-tax proceeds (the "Net Proceeds") from such
compensatory bonus shall be applied to the prepayment of the unpaid principal
balance plus all accrued and unpaid interest of this Note within seven (7)
calendar days after receipt thereof (the "Mandatory Prepayment Period"). If the
Lender does not receive such Net Proceeds within the Mandatory Prepayment
Period, the entire principal balance plus all accrued and unpaid interest of
this Note shall become immediately due and payable pursuant to Section 7 hereof.

        10. Mandatory Prepayment on Sale of Stock. If at any time, or from time
to time, Borrower shall receive any proceeds from the sale or other disposition
of shares of Lender capital stock now owned or hereinafter acquired by Borrower
("Borrower Stock"), then 50% of the after-tax proceeds (the "Borrower Stock
Proceeds") of such sale or other disposition shall be applied to the prepayment
of the unpaid principal balance plus all accrued and unpaid interest of this
Note within the Mandatory Prepayment Period. If the Lender does not receive such
Borrower Stock Proceeds within the Mandatory Prepayment Period, the entire
principal balance plus all accrued and unpaid interest of this Note shall become
immediately due and payable pursuant to Section 7 hereof.

        11. Recourse. The Lender shall be entitled to recourse against the
Borrower for the payment of any principal and accrued interest of the Note or
for any claim based hereon (including costs of collection).

        12. Costs of Collection. Upon the failure of the Borrower to pay any
amount due hereunder as and when due, the Borrower shall pay on demand any
reasonable costs and expenses incurred by the holder hereof in connection with
the collection of any outstanding principal and in connection with the
enforcement of any rights or remedies provided for pursuant to this Note. If not
paid on demand, all such costs and expenses automatically shall be added to the
remaining principal balance hereunder as of the date immediately following the
date of such demand.

<PAGE>

        13. Waiver. The Borrower hereby waives any right it might otherwise have
to require notice or acceptance by any other person of its obligations or
liabilities under this Note which are unconditional and absolute and waives
diligence, presentment, demand of payment, protest and notice with respect to
all of the obligations of the Borrower under this Note and with respect to any
action under this Note and all other notices and demands whatsoever, except as
specifically provided for in this Note. This Note may be amended, and the
observance of any term of this Note may be waived, with (and only with) the
written consent of the Lender.

        14. Governing Law. This Note shall be governed by and construed in
accordance with the laws of the State of California.

        15. Assignment or Pledge of Note. The Lender shall promptly notify the
Borrower of any endorsement, assignment, pledge or hypothecation of this Note to
a person not affiliated with the Lender. This Note may not be sold, assigned,
hypothecated, delegated or transferred by the Borrower, by operation of law or
otherwise, without prior written consent of the Lender.

        16. Loss, Mutilation, Etc. Upon notice from the holder of this Note to
the Borrower of the loss, theft, destruction or mutilation of this Note, and
upon receipt of an indemnity reasonably satisfactory to the Borrower from the
holder of this Note or, in the case of mutilation hereof, upon surrender of the
mutilated Note, the Borrower will make and deliver a new note of like tenor in
lieu of this Note.

        17. Notices. All notices and other communications required or permitted
under this Note shall be in writing and shall be personally delivered or sent by
certified first class United States mail, postage prepaid, return receipt
requested, and if mailed, shall be deemed to have been received on the third
business day after deposit in the mail, addressed to the Lender, Inktomi
Corporation, 4100 East 3rd Avenue, Foster City, California 94404, Attention:
General Counsel, or to the Borrower at the address set forth below the
Borrower's signature. Notice of any change of either party's address shall be
given by written notice in the manner set forth in this paragraph.

        18. Severability. If any provision in this Note is construed to be
invalid, illegal or unenforceable, then the remaining provisions shall not in
any way be affected thereby and shall be enforced without regard thereto.

<PAGE>
        IN WITNESS WHEREOF, the Borrower has executed this Note on the date
first above written.

BORROWER:

                                       /s/ David C. Peterschmidt
                                       -----------------------------------------
                                       Signature of Borrower

                                       -----------------------------------------
                                       Print or Type Name: David C. Peterschmidt

                                       ----------------------------------------
                                       Address

                                       -----------------------------------------
                                       City, State, Zip Code

                                       -----------------------------------------
                                       Telephone Number


AGREED AND ACCEPTED


Jerry Kennelly
-------------------------------------
Title: Chief Financial Officer

Inktomi Corporation
4100 East 3rd Avenue
Foster City, CA 94404