Second Amendment to
                     Agreement of Limited Partnership of
               Geodyne Energy Income Limited Partnership III-E


     This Second Amendment to Agreement of Limited Partnership of Geodyne Energy
Income  Limited  Partnership  III-E (the  "Partnership")  is entered into by and
between Geodyne Production Company  ("Production"),  a Delaware corporation,  as
General  Partner,   Geodyne  Depositary  Company   ("Depositary"),   a  Delaware
corporation,  as the  Limited  Partner,  and all  Substituted  Limited  Partners
admitted to the Partnership.

     WHEREAS,  on December  26, 1990,  Production  and  Depositary  executed and
entered into that certain  Agreement of Limited  Partnership of the  Partnership
(the "Agreement"); and

     WHEREAS,  on February 25, 1993,  Production  executed and entered into that
certain First Amendment to the Agreement  whereby it changed (i) the name of the
Partnership  from  "PaineWebber/Geodyne  Energy  Income  Partnership  III-E"  to
"Geodyne  Energy  Income  Limited  Partnership  III-E",  (ii) the address of the
Partnership's  principal  place of  business,  and  (iii)  the  address  for the
Partnership's agent for service of process; and

     WHEREAS,  Section 11.1 of the Agreement  provides that the General  Partner
may, without prior notice or consent of any Unit Holder,  amend any provision of
this  Agreement  if, in its  opinion,  such  amendment  does not have a material
adverse effect upon the Unit Holders; and

     WHEREAS,  Production as General  Partner  desires to amend the Agreement in
order to (i) expedite the method of accepting  transfers of Unit Holders'  Units
in   the   Partnership   and   (ii)   provide   for   an   optional   right   of
repurchase/redemption which may be exercised by the Unit Holders.


     NOW,  THEREFORE,   in  consideration  of  the  covenants,   conditions  and
agreements herein contained, the parties hereto hereby agree as follows:

I.     The third sentence  contained in Section 7.3 of the Agreement is hereby
       amended and restated as follows:

            Unit Holders becoming  Substituted Limited Partners will be admitted
            to the Partnership monthly.



                                      -1-
<PAGE>





II.    The second  sentence  contained  in Section 7.3 of the  Agreement,  which
       sentence  required  the  payment by Unit  Holders of a fee (not to exceed
       $100) for legal and administrative  costs associated with the transfer of
       a Partnership Unit, is hereby deleted.


III.   The first  sentence  contained  in  Section 8.1E  of the  Agreement  is
       hereby amended and restated as follows:

            Unless  otherwise  provided  by  the  General  Partner,   any  sale,
            assignment   or  transfer  of  Units  shall  be  recognized  by  the
            Partnership  as of the  first  business  day of the  calendar  month
            following the approval of such assignment or transfer by the General
            Partner, or as soon thereafter as practicable.


IV.    The second  sentence  of Section  8.1E of the  Agreement  referring  to
       quarterly approvals of transfers is hereby deleted.


V.     Section 8.3I  of the Agreement,  which section  required the payment by
       Unit Holders of a fee (not to exceed $50) for expenses  associated with
       a transfer is hereby deleted.


VI.    Section 8.2B(3) of the Agreement,  which section  required the payment by
       Unit  Holders of a fee (not to exceed $50) for expenses  associated  with
       the General  Partner's  acceptance  of a Substituted  Limited  Partner is
       hereby deleted.


VII.   The first full  sentence of Section  8.1(iv) of the Agreement is hereby
       amended and restated as follows:

            For purposes of this  subsection,  the "Permitted  Transfers"  shall
            mean:  (1) transfers in which the basis of the Units in the hands of
            the transferee is  determined,  in whole or in part, by reference to
            its  basis in the hands of the  transferor  or is  determined  under
            Section  732 of the Code;  (2)  transfers  at death;  (3)  transfers
            between members of a family (as defined in Section  267(c)(4) of the
            Code);  (4) the issuance of Units by or on behalf of the Partnership
            in exchange for cash, property or services; (5) distributions from a
            retirement  plan  qualified  under Section  401(a) of the Code;  (6)
            Block  Transfers;  and (7) transfers  pursuant to Article Fifteen of
            this Agreement.




                                      -2-
<PAGE>




VIII.  The Agreement is hereby  amended to provide for a new Article  Fifteen.
       Said Article Fifteen is hereby stated as follows:


                                 Article Fifteen

                   Optional Repurchase/Redemption Provisions

                Section 15.1.  Optional Repurchase Right.
                ----------------------------------------

                Any Unit Holder or  Substituted  Limited  Partner shall have the
            right, at his option, to present his Units to the General Partner or
            its  designated  Affiliate for  repurchase on the basis set forth in
            this Article Fifteen.

                Section 15.2.  Procedure for Repurchase.
                ---------------------------------------

                A.  As  of  December  31,  1992  and  annually  thereafter  (the
            "Appraisal  Date") the General  Partner  shall  appraise  the Proved
            Reserves  and  other  assets  of  the  Partnership  pursuant  to the
            provisions set forth herein and shall assign a repurchase price (the
            "Repurchase Price") to the Unit Holders' Units in the Partnership in
            accordance with the provisions set forth herein.

                B. In arriving at the Repurchase  Price,  the General  Partner
            shall  consider  those  factors  deemed  relevant by it including,
            without limitation, the following:

                (i)    the present  value of the  estimated  future
                       net  revenues  of the  Partnership's  Proved
                       Reserves,  calculated  as  described  below;
                       and

                (ii)   the  book  value  of all  other  Partnership
                       assets and liabilities.

                Section 15.3.  Calculation of Present Value of the
                               Partnership's Estimated Future Net Revenues.
                -----------------------------------------------------------

                In calculating the present value of the Partnership's  Estimated
            Future Net  Revenues  the General  Partner  shall use the  petroleum
            engineering reports and other petroleum reserve information required
            to be furnished to the Unit Holders pursuant to Section 10.4C of the
            Agreement.



                                      -3-
<PAGE>




                Future gross revenues expected to be derived from the production
            and sale of the Proved Reserves  attributable  to the  Partnership's
            Producing Properties shall be estimated using either (i) escalations
            of future  sales  prices of  Hydrocarbons  supplied  by the  General
            Partner (the "Escalated  Case") or (ii) sales prices of Hydrocarbons
            provided by Regulation  S-X adopted by the  Securities  and Exchange
            Commission (the "SEC Case"), as the General Partner may determine in
            its sole discretion.

                Future net revenues shall be calculated by deducting anticipated
            expenses  (using either (i)  escalations of future costs supplied by
            the General  Partner if the General  Partner  adopted the  Escalated
            Case with  respect to future sales  prices of  Hydrocarbons  or (ii)
            constant  future costs if the General  Partner  adopted the SEC Case
            with respect to future sales prices of Hydrocarbons)  from estimated
            future gross revenues.

                The present value of the future net revenues shall be calculated
            by discounting  the estimated  future net revenues at either 10% (if
            the General Partner  employed future pricing  criteria in accordance
            with the SEC Case) or that rate per  annum  which is one  percentage
            point higher than the prime rate of interest of The Chase  Manhattan
            Bank,  N.A. or any successor  bank, as of the Appraisal Date (if the
            General  Partner  employed  pricing  criteria in accordance with the
            Escalated Case, provided,  however, that such discount rate will not
            exceed 18% per annum and will be no less than 10% per annum).

                Section 15.4.  Risk Reduction.
                -----------------------------

                In determining the Repurchase Price for Unit Holders pursuant to
            this Article Fifteen,  the present value of the Partnership's Proved
            Developed  Producing  Reserves  shall be reduced by 25% for risk and
            the present value of all other  categories of Proved  Reserves shall
            be reduced by 35% for risk. The risk reductions  shall be subject to
            upward or downward  adjustment by the General Partner if, during the
            period between the Appraisal Date and the Effective Date (as defined
            in Section 15.5),  there has been a material increase or decrease in
            the current  price of oil or gas or in the  estimated  amount of the
            Partnership's Proved Reserves.



                                      -4-
<PAGE>




                Section 15.5.  Tender Procedure.
                -------------------------------

                Upon completion of the appraisal of the Partnership's  assets as
            of the Appraisal  Date,  the General  Partner shall notify each Unit
            Holder of the Repurchase Price and his  proportionate  share thereof
            and either the General  Partner or one of its Affiliates  will offer
            to  purchase  such Unit  Holder's  Units in  exchange  for such Unit
            Holder's  proportionate share of the Repurchase Price (a "Repurchase
            Offer").  Any  Unit  Holder  desiring  to  do  so  may  accept  such
            Repurchase  Offer by notifying the General  Partner of his election.
            Unit Holders so notifying  the General  Partner shall be referred to
            herein as  "Electing  Unit  Holders".  The  General  Partner  or its
            designated  Affiliate shall thereupon  promptly pay to each Electing
            Unit Holder, his proper share of the Repurchase Price, calculated as
            herein  set  forth,  within 30 days from the date  which a  properly
            drawn assignment of such Electing Unit Holder's  interest,  free and
            clear of all liens and encumbrances,  is tendered to and accepted by
            the General  Partner or its  designated  Affiliate  (the  "Effective
            Date"). Upon the acquisition of an Electing Unit Holder's Units, the
            General  Partner  or  its  designated  Affiliate  shall,  as of  the
            Effective  Date of such  acquisition,  succeed to all the rights and
            obligations attributable to such interest.

                 Section 15.6.  Monthly Adjustment to Repurchase Price.
                 ------------------------------------------------------

                 The  Repurchase  Price shall be  recalculated  monthly with the
            Repurchase   Price   being   reduced  by  the  amount  of  any  cash
            distributions  to Unit Holders  during the period from the Appraisal
            Date to the date of the  payment of the  Repurchase  Price and shall
            otherwise  be adjusted to reflect the effect of material  operations
            during such period, including a material increase or decrease in the
            current  price  of oil or gas  or in  the  estimated  amount  of the
            Partnership's Proved Reserves.  In the event the Repurchase Price is
            adjusted  for any reason  other than to reflect  the payment of cash
            distributions,   the   General   Partner   shall   provide   written
            notification  of such  adjustment  to the Unit  Holders at least ten
            (10) business days prior to acceptance of Units for purchase.



                                      -5-
<PAGE>




                Section 15.7.  Limitation on Units Repurchased.
                -----------------------------------------------

                A. At the sole  discretion of the General  Partner,  the General
            Partner or its  designated  Affiliate  may either (i) limit the time
            period in which it will accept tendered Units for repurchase or (ii)
            limit the amount of Units to be accepted for  repurchase;  provided,
            however,  that in any event the  annual  repurchase  offer  will (i)
            remain  open  for at least  thirty  (30)  days and (ii) the  General
            Partner  or  its   designated   Affiliate  will  offer  to  annually
            repurchase (and will purchase validly  presented Units) at least 10%
            of the  outstanding  Units  of the  Partnership.  In the  event  the
            General  Partner or its designated  Affiliate  imposes a limitation,
            the General  Partner will either (i) specify such  limitation(s)  in
            the  annual  Repurchase  Offer  mailed to the Unit  Holders  or (ii)
            provide  all  Unit  Holders  with  written   notification   of  such
            limitation(s)  at least thirty (30) days prior to the effective date
            of any such limitation(s).

                B. In the event the General  Partner  imposes a limitation  upon
            the number of Units to be  repurchased in the  Partnership,  and the
            amount  of  Units  tendered,  but  not  repurchased,   exceeds  such
            limitation,  such tendered  Units will be accepted for repurchase by
            lot.

                C. In addition,  in order to avoid certain  possible adverse tax
            consequences,  the General  Partner may, in order to comply with the
            regulations  or  procedures  under  Section  469(k) of the  Internal
            Revenue  Code of 1986,  as  amended,  relating to  "publicly  traded
            partnerships,"  (i)  delay  or  defer  the  Effective  Date  of  any
            repurchase  and  (ii)  limit  the  total  number  of  Units  of  any
            Partnership to be repurchased in any 12-month  period to the maximum
            number provided in such regulations and procedures.  In the event of
            such  delay or  deferral,  the  General  Partner  shall  notify  the
            Electing  Unit Holder of the reasons  therefor and shall provide the
            Electing Unit Holder with the option to withdraw his tender of Units
            for repurchase.



                                      -6-
<PAGE>




       IN WITNESS  WHEREOF,  the parties hereto have hereunto set their hands as
of the 4th day of August, 1993.

                                       Geodyne Production Company
                                       as General Partner

                                       By:  /s/ C. Philip Tholen
                                            ----------------------------
                                            C. Philip Tholen
                                            President

                                       Geodyne Depositary Company, as the
                                       Limited Partner


                                       By:  /s/ Dennis R. Neill
                                            ----------------------------
                                            Dennis R. Neill
                                            Senior Vice President

                                       Geodyne Production Company, as
                                       Attorney-in-Fact for all Substituted
                                       Limited Partners


                                       By:  /s/ Drew S. Phillips
                                            ----------------------------
                                            Drew S. Phillips
                                            Vice President - Controller


                                      -7-