<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM 10-K


           [ X ] ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934
                   For the Fiscal Year Ended December 31, 1998

                                       OR

          [ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934
        For the Transition Period from ______________ to ________________


                         Commission File Number 0-13546


                     APACHE OFFSHORE INVESTMENT PARTNERSHIP

           A Delaware                                     IRS Employer
           General Partnership                          No. 41-1464066

                              One Post Oak Central
                       2000 Post Oak Boulevard, Suite 100
                            Houston, Texas 77056-4400

                         Telephone Number (713) 296-6000


        SECURITIES REGISTERED PURSUANT TO SECTION 12(b) OF THE ACT: NONE


           SECURITIES REGISTERED PURSUANT TO SECTION 12(g) OF THE ACT:
                                PARTNERSHIP UNITS


         Indicate by check mark whether the Partnership (1) has filed all
reports required to be filed by Section 13 or 15(d) of the Securities Exchange
Act of 1934 during the preceding 12 months (or for such shorter period that the
Partnership was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.

                        YES      X            NO
                               -----                 ----


         Indicate by check mark if disclosure of delinquent filers pursuant to
Item 405 of Regulation S-K is not contained herein, and will not be contained,
to the best of Partnership's knowledge, in definitive proxy or information
statements incorporated by reference in Part III of this Form 10-K or any
amendment to this Form 10- K.   X
                              -----

                      DOCUMENTS INCORPORATED BY REFERENCE:

         Portions of Apache Corporation's proxy statement relating to its 1999
annual meeting of shareholders have been incorporated by reference into Part III
hereof.



<PAGE>   2


                                TABLE OF CONTENTS

                                   DESCRIPTION

<TABLE>
<CAPTION>
ITEM                                                                                                             PAGE
----                                                                                                             ----
                                     PART I
<S>           <C>                                                                                               <C>
   1.         BUSINESS......................................................................................       1
   2.         PROPERTIES....................................................................................       4
   3.         LEGAL PROCEEDINGS.............................................................................       4
   4.         SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS...........................................       4


                                     PART II

   5.         MARKET FOR THE PARTNERSHIP'S SECURITIES AND RELATED
                   SECURITY HOLDER MATTERS..................................................................       5
   6.         SELECTED FINANCIAL DATA.......................................................................       5
   7.         MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
                   CONDITION AND RESULTS OF OPERATIONS......................................................       6
   8.         FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA...................................................      11
   9.         CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON
                   ACCOUNTING AND FINANCIAL DISCLOSURE......................................................      25


                                    PART III

  10.         DIRECTORS AND EXECUTIVE OFFICERS OF THE PARTNERSHIP...........................................      25
  11.         EXECUTIVE COMPENSATION........................................................................      25
  12.         SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS
                   AND MANAGEMENT...........................................................................      25
  13.         CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS................................................      25


                                     PART IV

  14.         EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND REPORTS ON FORM 8-K...............................      26
</TABLE>

         All defined terms under Rule 4-10(a) of Regulation S-X shall have their
statutorily-prescribed meanings when used in this report. Quantities of natural
gas are expressed in this report in terms of thousand cubic feet (Mcf), million
cubic feet (MMcf) or billion cubic feet (Bcf). Oil is quantified in terms of
barrels (bbls), thousands of barrels (Mbbls) and millions of barrels (MMbbls).
Natural gas is compared to oil in terms of barrels of oil equivalent (boe) or
million barrels of oil equivalent (MMboe). Oil and natural gas liquids are
compared with natural gas in terms of million cubic feet equivalent (MMcfe) and
billion cubic feet equivalent (Bcfe). One barrel of oil is the energy equivalent
of six Mcf of natural gas. Daily oil and gas production is expressed in terms of
barrels of oil per day (bopd) and thousands of cubic feet of gas per day (Mcfd),
respectively. With respect to information relating to the Partnership's working
interest in wells or acreage, "net" oil and gas wells or acreage is determined
by multiplying gross wells or acreage by the Partnership's working interest
therein. Unless otherwise specified, all references to wells and acres are
gross.



<PAGE>   3



                                     PART I


ITEM 1. BUSINESS

GENERAL

     Apache Offshore Investment Partnership (the Investment Partnership), a
Delaware general partnership, was organized in October 1983, with public
investors as Investing Partners and Apache Corporation (Apache), a Delaware
corporation, as Managing Partner. The operations of the Investment Partnership
are conducted by Apache Offshore Petroleum Limited Partnership (the Limited
Partnership), a Delaware limited partnership, of which Apache is the sole
general partner and the Investment Partnership is the sole limited partner.

     The Investing Partners purchased Units of Partnership Interests (Units) in
the Investment Partnership at $150,000 per Unit, with five percent down and the
balance in payments as called by the Investment Partnership. As of December 31,
1998, a total of $85,000 had been called for each Unit. In 1989, the Investment
Partnership determined that the full $150,000 per Unit was not needed, fixed the
total calls at $85,000 per Unit, and released the Investing Partners from
liability for future calls. The Investment Partnership invested, and will
continue to invest, its entire capital in the Limited Partnership. As used
hereafter, the term "Partnership" refers to either the Investment Partnership or
the Limited Partnership, as the case may be.

     The Partnership's business is participation in oil and gas exploration,
development and production activities on federal lease tracts in the Gulf of
Mexico, offshore Louisiana and Texas. Except for the Matagorda Island Block 681
and 682 interests, as described below, the Partnership acquired its oil and gas
interests through the purchase of 85 percent of the working interests held by
Apache as a participant in a venture (the Venture) with Shell Oil Company
(Shell) and certain other companies. The Partnership owns working interests
ranging from 6.29 percent to 9.44 percent in the Venture's properties.

     The Venture acquired substantially all of its oil and gas properties
through bidding for leases offered by the federal government. The Venture
members relied on Shell's knowledge and expertise in determining bidding
strategies for the acquisitions. When Shell was successful in obtaining the
properties, it generally billed participating members on a promoted basis
(one-third for one-quarter) for the acquisition of exploratory leases and on a
straight-up basis for the acquisition of leases defined as drainage tracts. All
such billings were proportionately reduced to each member's working interest.

     In November 1992, Apache and the Partnership formed a joint venture to
acquire Shell's 92.6 percent working interest in Matagorda Island Blocks 681 and
682 pursuant to a jointly-held contractual preferential right to purchase.
Apache and the Partnership previously owned working interests in the blocks
equal to 1.109 percent and 6.287 percent, respectively, and net revenue
interests of .924 percent and 5.239 percent, respectively. To facilitate the
acquisition, Apache and the Partnership contributed all of their interests in
Matagorda Island Blocks 681 and 682 to a newly formed joint venture, and Apache
contributed $64.6 million ($55.6 million net of purchase price adjustments) to
the joint venture to finance the acquisition. The Partnership had neither the
cash nor additional financing to fund its proportionate share of the acquisition
and participated through an increased net revenue interest in the joint venture.

     Under the terms of the joint venture agreement, the Partnership's effective
net revenue interest in the Matagorda Island Block 681 and 682 properties
increased to 13.284 percent as a result of the acquisition, while its working
interest was unchanged. The acquisition added approximately 7.5 Bcf of natural
gas and 16 Mbbls of oil to the Partnership's reserve base without any
incremental expenditures by the Partnership.

     Since the Venture is not expected to acquire any additional exploratory
acreage, future acquisitions, if any, will be confined to those leases defined
as drainage tracts. The current Venture members would pay their proportionate
share of acquiring any drainage tracts on a non-promoted basis.


                                       1

<PAGE>   4



     Offshore exploration differs from onshore exploration in that production
from a prospect generally will not commence until a sufficient number of
productive wells have been drilled to justify the significant costs associated
with construction of a production platform. Exploratory wells usually are
drilled from mobile platforms until there are sufficient indications of
commercial production to justify construction of a permanent production
platform.

     Apache, as Managing Partner, manages the Partnership's operations. Apache
uses a portion of its staff and facilities for this purpose and is reimbursed
for actual costs paid on behalf of the Partnership, as well as for general,
administrative and overhead costs properly allocable to the Partnership.

1998 BUSINESS DEVELOPMENT

     The Partnership spud five new wells in 1998. Two developmental wells were
drilled at South Pass Block 83. Both of these wells were sidetracked, completed
and began producing in 1998. A third well spud in 1997 was drilled to total
depth in 1998 and abandoned.

     An exploratory well at North Padre Island Block 976 was drilled and
temporarily abandoned in 1998, and was being evaluated at December 31, 1998. A
developmental well was also drilled and sidetracked and is expected to be
completed in 1999. Additionally, an exploratory well was drilled and abandoned
in 1998 at North Padre Island Block 969.

     At South Timbalier Block 295, a developmental well spud in 1997 was
completed and began production. In addition, a water-injection well spud in 1996
at South Timbalier Block 295 was completed and initiated in 1998.

     In early 1998, the Partnership completed an exploratory well spud in 1997
at Matagorda Island Block 705. This well was recompleted in mid-1998 and
returned to production late in the year. In addition, a developmental well spud
in 1997 was completed and began production at Ship Shoal Block 259.

     Since inception, the Partnership has acquired an interest in 49 prospects.
As of December 31, 1998, 42 of those prospects have been surrendered or sold.

     The status of the Partnership's 49 original prospects is shown in the
following table:

<TABLE>
<CAPTION>
                                                AS OF DECEMBER 31,
                                              ---------------------
                                                1998         1997
                                              --------     --------
<S>                                           <C>          <C>
Prospect Status
---------------

Producing - fully developed                          6            7
Producing - partially developed                      1            3
                                              --------     --------

Total discoveries                                    7           10
Surrendered/sold                                    42           39
                                              --------     --------

Total                                               49           49
                                              ========     ========
</TABLE>

     As of December 31, 1998, 115 wells have been drilled on the seven remaining
prospects. Of the 115 wells, 90 were productive and of those, 77 are currently
producing. Fifteen of the Partnership's producing wells are dual completions.
The Partnership had, at December 31, 1998, estimated proved oil and gas reserves
of 15.3 Bcfe, of which 67 percent was natural gas.

     In January 1998, the Partnership sold its interest in the Krypton Prospect
(West Cameron Block 368). Additionally, the Partnership relinquished its
overriding royalty interests in the Cortez Prospect (Matagorda Island Block 588)
in August 1998 and in the Topaz Prospect (Vermillion Block 95) in October 1998.


                                       2


<PAGE>   5



FULL COST CEILING TEST

     Under the full cost accounting rules of the Securities and Exchange
Commission (SEC), the Partnership reviews the carrying value of its oil and gas
properties each quarter. Under full cost accounting rules, capitalized costs of
proved oil and gas properties may not exceed the present value of estimated
future net revenues from proved reserves, discounted at 10 percent, plus the
lower of cost or fair market value of unproved properties included in the costs
being amortized, if any. Application of these rules generally requires pricing
future production at the unescalated oil and gas prices in effect at the end of
each fiscal quarter and requires a write-down if the "ceiling" is exceeded, even
if prices declined for only a short period of time. The Partnership had no
write-downs during 1998 due to ceiling test limitations.

MARKETING

     Apache, on behalf of the Partnership, seeks and negotiates oil and gas
marketing arrangements with various marketers and purchasers. During 1998, the
Partnership's spot market gas was purchased primarily by Producers Energy
Marketing LLC (ProEnergy) and the Partnership's oil and condensate production
was purchased primarily by Plains Petroleum Operating Co. (Plains Petroleum). In
June 1998, Apache formed a strategic alliance with Cinergy Corp. (Cinergy) to
market substantially all of Apache's natural gas production from North America
and sold its 57 percent interest in ProEnergy to Cinergy. ProEnergy will
continue to market Apache's North American natural gas production for 10 years,
with an option to terminate after six years, under an amended and restated gas
purchase agreement effective July 1, 1998. The prices the Partnership received
for its gas production prior to the sale of ProEnergy were, in the opinion of
Apache, comparable to the prices that would have been received from a
non-affiliated party. The prices the Partnership received after the sale of
ProEnergy and will continue to receive for its gas production, in the opinion of
Apache, approximate market prices.

     See Note (5) "Major Customer Information" to the Partnership's financial
statements under Item 8. Because the Partnership's oil and gas products are
commodities and the prices and terms of its sales reflect those of the market,
the Partnership does not believe that the loss of any customer would have a
material adverse affect on the Partnership's business or results of operations.
The Partnership is not in a position to predict future oil and gas prices.

ENVIRONMENTAL

     The Partnership, as an owner or lessee of interests in oil and gas
properties, is subject to various federal, state and local laws and regulations
relating to the discharge of materials into, and protection of, the environment.
These laws and regulations may, among other things, impose liability on the
lessee under an oil and gas lease for the cost of pollution clean-up resulting
from operations, subject the lessee to liability for pollution damages and
require suspension or cessation of operations in affected areas.

     The Partnership has made and will continue to make expenditures in its
efforts to comply with these requirements. These costs are inextricably
connected to normal operating expenses such that the Partnership is unable to
separate the expenses related to environmental matters; however, the Partnership
does not believe such expenditures are material to its financial position or
results of operations.

     The Partnership does not believe that compliance with federal, state or
local provisions regulating the discharge of materials into the environment, or
otherwise relating to the protection of the environment, will have a material
adverse effect upon the capital expenditures, earnings and the competitive
position of the Partnership, but there is no assurance that changes in or
additions to laws or regulations regarding the protection of the environment
will not have such an impact.

COMPETITION

     The Partnership is a very minor factor in the oil and gas industry in the
Gulf of Mexico area and faces strong competition from much larger producers for
the marketing of its oil and gas. The Partnership's ability to compete for
purchasers and favorable marketing terms will depend on the general demand for
oil and gas from Gulf of Mexico producers. More particularly, it will depend
largely on the efforts of Apache to find the best markets.


                                       3

<PAGE>   6
ITEM 2. PROPERTIES

     Acreage is held by the Partnership pursuant to the terms of various leases.
The Partnership does not anticipate any difficulty in retaining any of its
desirable leases. A summary of the Partnership's producing wells and gross
acreage as of December 31, 1998, is set forth below:

<TABLE>
<CAPTION>
                                                                                                              
                                                            PRODUCING                              ACRES
                                                          OIL/GAS WELLS      AVERAGE     ---------------------------
                                                        ------------------   WORKING     DEVELOPED     UNDEVELOPED
        LEASE BLOCK              PROSPECT       STATE    GROSS      NET     INTEREST       GROSS          GROSS
----------------------------- ----------------  ------- --------  -------- ------------  -----------  --------------
<S>                           <C>               <C>     <C>       <C>      <C>          <C>           <C>
Ship Shoal 258, 259           Genesis             LA       11        .7      .0628698       10,141              --
South Timbalier 276, 295      Grover              LA       24       1.7      .0708333       10,000              --
North Padre Island 969, 976   Rosita              TX       13        .9      .0708333       11,520           5,760
Matagorda Island 681, 682,    Roberto             TX       18       1.1      .0789697       11,880              --
705
South Pass 83, 74             Manx                LA        7        .5      .0678914        7,500              --
East Cameron 60               East Aragonite      LA        1        .1      .0944444        5,000              --
Ship Shoal 201, 202           Bromeliad           LA        3        --          ORRI       10,000              --
                                                        -----  --------                  ---------      ----------

                                                           77       5.0                     66,041           5,760
                                                        =====  ========                  =========      ==========
</TABLE>

     In January 1998, the Partnership sold its interest in the Krypton Prospect
(West Cameron Block 368). The Partnership relinquished its overriding royalty
interests in the Cortez Prospect (Matagorda Island Block 588) and the Topaz
Prospect (Vermillion Block 95) in August 1998 and October 1998, respectively.
See Note (4) "Oil and Gas Properties" to the Partnership's financial statements
for costs incurred in oil and gas development and production activities. See
Supplemental Oil and Gas Disclosures under Item 8 for related reserve
information. On a net revenue basis, the Partnership owns five wells.

PRODUCTION AND PRICING DATA

     The following table describes, for each of the last three fiscal years, oil
and gas production for the Partnership, average production costs (excluding
severance taxes) and average sales prices.

<TABLE>
<CAPTION>
                                     PRODUCTION                                      AVERAGE SALES PRICES
                              --------------------------        AVERAGE           --------------------------
           YEAR ENDED           OIL             GAS            PRODUCTION            OIL             GAS
          DECEMBER 31,        (MBBLS)          (MMCF)         COST PER MCFE       (PER BBL)       (PER MCF)
          --------------      ----------     -----------     ----------------     -----------     -----------
          <S>                  <C>            <C>            <C>                  <C>              <C>
              1998                 106            3,127          $     .27        $   12.40       $     2.08
              1997                 125            3,878                .10            19.30             2.49
              1996                 164            5,651                .18            20.73             2.50
</TABLE>

     See the Supplemental Oil and Gas Disclosures under Item 8 for estimated oil
and gas reserves quantities.

ITEM 3. LEGAL PROCEEDINGS

     There are no material legal proceedings pending to which the Partnership is
a party or to which the Partnership's interests are subject.

ITEM 4. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

     There were no matters submitted to a vote of security holders during the
fourth quarter of 1998.


                                       4

<PAGE>   7



                                     PART II


ITEM 5. MARKET FOR THE PARTNERSHIP'S SECURITIES AND RELATED SECURITY HOLDER
        MATTERS

     As of December 31, 1998, there were 1,141.0 of the Partnership's Units
outstanding held by approximately 934 investors of record. The Partnership has
no other class of security outstanding or authorized. The Units are not traded
on any security market. Cash distributions totaled approximately $1.7 million,
or $1,500 per Unit, during 1998 and approximately $5.4 million, or $4,500 per
Unit, during 1997.

     As discussed in Item 7, an amendment to the Partnership Agreement in
February 1994 created a right of presentment under which all Investing Partners
have a limited and voluntary right to offer their Units to the Partnership twice
each year to be purchased in cash.


ITEM 6. SELECTED FINANCIAL DATA

     The following selected financial data for the five years ended December 31,
1998, should be read in conjunction with the Partnership's financial statements
and related notes included under Item 8.

<TABLE>
<CAPTION>
                                                             AS OF OR FOR THE YEAR ENDED DECEMBER 31,
                                                  ------------------------------------------------------------
                                                    1998         1997         1996         1995         1994
                                                  --------     --------     --------     --------     --------
                                                            (In thousands, except per Unit amounts)
<S>                                               <C>          <C>          <C>          <C>          <C>
Total assets                                      $  9,841     $ 10,524     $ 12,252     $ 13,486     $ 14,291
                                                  ========     ========     ========     ========     ========

Long-term debt                                    $     --     $     --     $  1,998     $  7,310     $  9,435
                                                  ========     ========     ========     ========     ========

Partners' capital                                 $  9,080     $  8,647     $  8,498     $  5,472     $  4,175
                                                  ========     ========     ========     ========     ========

Oil and gas sales                                 $  7,827     $ 12,067     $ 17,511     $ 13,138     $ 16,926
                                                  ========     ========     ========     ========     ========

Net income                                        $  3,621     $  8,244     $ 11,127     $  6,214     $ 10,116
                                                  ========     ========     ========     ========     ========

Net income allocated to:
    Managing Partner                              $  1,061     $  1,967     $  2,652     $  1,800     $  2,519
    Investing Partners                               2,560        6,277        8,475        4,414        7,597
                                                  --------     --------     --------     --------     --------

                                                  $  3,621     $  8,244     $ 11,127     $  6,214     $ 10,116
                                                  ========     ========     ========     ========     ========

Net income per Investing
    Partner Unit                                  $  2,193     $  5,260     $  7,032     $  3,584     $  5,974
                                                  ========     ========     ========     ========     ========

Cash distributions per
    Investing Partner Unit                        $  1,500     $  4,500     $  4,500     $  2,250     $  4,500
                                                  ========     ========     ========     ========     ========
</TABLE>


                                       5

<PAGE>   8



ITEM 7. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
        OF OPERATIONS

     The Partnership's 1998 net income per Investing Partner Unit was lower than
1997. In addition to reduced production volumes, lower average oil and gas
prices significantly impacted net income. The average natural gas price was 16
percent lower than the average price in 1997, while the average crude oil price
declined 36 percent from 1997. Lease operating expense (LOE) was significantly
higher in 1998, partially offset by lower depreciation, depletion and
amortization (DD&A) expense. Distributions per Investing Partner Unit made in
1998 were significantly lower than 1997.


RESULTS OF OPERATIONS

NET INCOME AND REVENUE

     The Partnership reported net income of $3.6 million for 1998 versus $8.2
million in 1997. Net income per Investing Partner Unit decreased 58 percent, to
$2,193 from $5,260. The impact on net income of lower production volumes, lower
oil and gas prices and higher LOE during 1998 was partially offset by lower DD&A
expense.

     Revenues decreased 36 percent, from $12.2 million in 1997, to $7.9 million
in 1998. Natural gas and crude oil sales contributed approximately 82 percent
and 17 percent, respectively, to the Partnership's total revenue in 1998. The
Partnership is not in a position to predict future oil and gas prices.

     The Partnership's oil and gas production volume and price information is
summarized in the following table:

<TABLE>
<CAPTION>

                                                FOR THE YEAR ENDED
                                                   DECEMBER 31,
                                      -----------------------------------
                                         1998         1997       DECREASE
                                      ----------   ----------    --------
<S>                                   <C>         <C>          <C>  
     Gas volumes - Mcf per day           8,567       10,625       (19%)
     Average gas price - per Mcf         $2.08        $2.49       (16%)
     Oil volume - barrels per day          291          341       (15%)
     Average oil price - per barrel     $12.40       $19.30       (36%)
</TABLE>

     Continued declines in production can be expected due to normal depletion.
It is not anticipated that the Partnership will acquire any additional
exploratory leases or that significant exploratory drilling will take place on
leases in which the Partnership currently holds interests.


1998 COMPARED TO 1997

     Natural gas sales for 1998 totaled $6.5 million, 33 percent lower than in
1997. The decrease was driven by lower average prices and lower production
volumes. The decrease in production volumes resulted primarily from normal
declines at Matagorda Island Block 681 and North Padre Island Block 969 and the
sale of West Cameron Block 368.

     The Partnership's crude oil sales for 1998 totaled $1.3 million, a 45
percent decrease from 1997. The average realized price for 1998 decreased 36
percent when compared to 1997. In addition to the decrease in crude oil prices
was a 15 percent decline in production versus 1997. The decrease in oil
production resulted primarily from normal decline at East Cameron Block 60 and
downtime for drilling operations at Ship Shoal Block 259.

     Given the small number of producing wells owned by the Partnership, and the
fact that offshore wells tend to decline at a faster rate than onshore wells,
the Partnership's future production will be subject to more volatility than
those entities with greater reserves and longer-lived properties.


                                       6

<PAGE>   9

OPERATING EXPENSES

         The Partnership's DD&A rate, expressed as a percentage of oil and gas
sales, was approximately 35 percent during 1998, up from 25 percent for 1997.
The increase in the DD&A rate was a result of decreased natural gas and crude
oil prices. Overall, 1998 DD&A expense of $2.7 million decreased by $.3 million
when compared to 1997 due to lower production in the current period.

     LOE of $1.0 million increased by $.6 million during 1998 when compared to
1997. The increase in LOE was the result of higher workover activity in 1998 and
non-recurring credits received from joint venture audits in 1997.


1997 COMPARED TO 1996

     Natural gas sales for 1997 totaled $9.7 million, 31 percent lower than in
1996. The decrease was driven by lower production volumes due to normal declines
in production, downtime for drilling at South Timbalier Block 295, and downtime
for drilling and compressor installation work at Ship Shoal Block 259. Also
contributing to the decline was the Partnership taking less than its entitlement
at South Pass Block 83 and North Padre Island Block 969, where make-up volumes
were taken by underproduced working interest owners.

     The Partnership's crude oil sales for 1997 totaled $2.4 million, a 29
percent decrease from 1996. The average realized price for 1997 decreased seven
percent when compared to 1996. In addition to the decrease in crude oil prices
was a 24 percent decline in production versus 1996. The decrease in oil
production resulted primarily from normal decline at East Cameron Block 60 and
downtime for drilling operations at South Timbalier Block 295.

OPERATING EXPENSES

     Primarily as a result of lower oil and gas production, DD&A expense for
1997 decreased 31 percent from 1996. The Partnership's DD&A rate, expressed as a
percentage of oil and gas sales, was 25 percent during each of 1997 and 1996.

     LOE of $.4 million decreased by $.8 million, or 63 percent, during 1997
when compared to 1996. The reduction in LOE in 1997 was the result of lower
workover activity and non-recurring credits received from joint venture audits
in 1997.

     Interest expense for 1997 included only one month of interest, as the
Partnership repaid the outstanding debt balance and terminated its revolving
credit facility on January 31, 1997.


CASH FLOW, LIQUIDITY AND CAPITAL RESOURCES

CAPITAL COMMITMENTS

     The Partnership's primary needs for cash are for operating expenses,
drilling and recompletion expenditures, distributions to Investing Partners, and
the purchase of Units offered by Investing Partners under the right of
presentment. The Partnership used cash from operating activities in 1997 and
1996 to reduce debt by $2.0 million and $5.3 million, respectively. The
Partnership had no outstanding debt at December 31, 1998.

     During 1998, the Partnership's oil and gas property additions totaled $2.3
million. The 1998 additions include drilling activity on a water-injection well
and a developmental well at South Timbalier Block 295. In addition, one
developmental well was drilled at Ship Shoal Block 259, and one exploratory well
was completed at Matagorda Island Block 705. At South Pass Block 83, two
sidetrack developmental wells were drilled, and one sidetrack developmental and
two exploratory wells were drilled at North Padre Island Blocks 976 and 969.
Additions to oil and gas properties totaled $4.0 million and $1.1 million in
1997 and 1996, respectively.


                                       7

<PAGE>   10



     The Partnership anticipates capital expenditures will total approximately
$1.7 million in 1999, based on preliminary information provided by the operators
of the properties in which the Partnership has interests. The anticipated
capital expenditures relate primarily to recompletions at South Timbalier Block
295 and completions at North Padre Island Block 976. Additional capital
expenditures may be proposed by the operators in the future.

     During 1998, the Partnership paid distributions to Investing Partners
totaling approximately $1.7 million or $1,500 per Unit, which is 67 percent
lower than the per Unit distribution in 1997. The Partnership made a
distribution of $750 per Unit in March 1999. Apache, as the Managing Partner,
will review the possibility of a distribution in October 1999. Future
distributions will be dependent on actual and expected production levels,
realized and expected oil and gas prices and actual and anticipated capital
expenditures.

     In February 1994, an amendment to the Partnership Agreement created a right
of presentment under which all Investing Partners have a limited and voluntary
right to offer their Units to the Partnership twice each year to be purchased
for cash. In 1998, the first right of presentment offer of $11,161 per Unit,
plus interest to the date of payment, was made to Investing Partners based on a
December 31, 1997 valuation date. The second right of presentment offer of
$9,824 per Unit, plus interest to the date of payment, was made to the Investing
Partners based on a valuation date of June 30, 1998. As a result, the
Partnership acquired 43.22 Units for a total of approximately $487,000 in cash.
In 1997 and 1996, Investing Partners were paid approximately $180,000 and
$162,000, respectively, for a total of 28.16 Units.

     There will be two rights of presentment in 1999, but the Partnership is not
in a position to predict how many Units will be presented for repurchase and
cannot, at this time, determine if the Partnership will have sufficient funds
available to repurchase Units. The Amended Partnership Agreement contains
limitations on the number of Units that the Partnership can repurchase,
including an annual limit on repurchases of 10 percent of outstanding Units. The
Partnership has no obligation to repurchase any Units presented to the extent
that it determines that it has insufficient funds for such repurchases.

CAPITAL RESOURCES AND LIQUIDITY

     The Partnership's primary capital resource is net cash provided by
operating activities, which was $6.9 million for 1998, a decrease of 40 percent
from 1997, reflecting declines in oil and gas production and prices and higher
LOE. Future operating cash flows will be influenced by oil and gas prices and
production which cannot be determined at this time.

     The Partnership's future financial condition and results of operations will
largely depend upon prices received for its oil and natural gas production and
the costs of acquiring, finding, developing and producing reserves. A
substantial portion of the Partnership's production is sold under
market-sensitive contracts. Prices for oil and natural gas are subject to
fluctuations in response to changes in supply, market uncertainty and a variety
of factors beyond the Partnership's control. These factors include worldwide
political instability (especially in the Middle East), the foreign supply of oil
and natural gas, the price of foreign imports, the level of consumer demand and
the price and availability of alternative fuels. With natural gas accounting for
83 percent of the Partnership's 1998 production and 67 percent of total proved
reserves, on an energy equivalent basis, the Partnership is affected more by
fluctuations in natural gas prices than in oil prices.

     It is expected that the net cash provided by operating activities will be
sufficient to meet the Partnership's liquidity needs for routine operations over
the next two years. However, in the event that future short-term operating cash
requirements are greater than the Partnership's financial resources, the
Partnership will seek short-term, interest-bearing advances from the Managing
Partner as needed.

     In accordance with the Partnership's continuing objectives to maximize unit
holder value and cash distributions, the Managing Partner plans to re-evaluate
the future of the Partnership following this year's capital investments.



                                       8


<PAGE>   11


IMPACT OF THE YEAR 2000 ISSUE

       The inability of some computer programs and embedded computer chips to
distinguish between the year 1900 and the year 2000 (the Year 2000 issue) poses
a serious threat of business disruption to any organization that utilizes
computer technology and computer chip technology in their business systems or
equipment. Apache, as Managing Partner, manages the Partnership's operations.
Apache uses a portion of its staff for this purpose and is reimbursed for actual
costs paid on behalf of the Partnership, as well as for general, administrative
and overhead costs properly allocable to the Partnership. Apache has formed a
Year 2000 Task Force with representation from major business units to inventory
and assess the risk of hardware, software, telecommunications systems, office
equipment, embedded chip controls and systems, process control systems, facility
control systems and dependencies on external trading partners. The project
phases, expected completion dates and percentage complete as of March 1999 are
as follows:

<TABLE>
<CAPTION>
                          PHASE                              COMPLETION DATE              PERCENT COMPLETE
          ---------------------------------------          --------------------         --------------------
<S>                                                       <C>                          <C> 
          Organization                                             July 1998                   100%

          Assessment                                           November 1998                   100%
              Desktop Computers
              Network Hardware
              Software
              Embedded Systems
              External Trading Partners
              Building/Infrastructure Systems
              Telecommunications Systems

          Implementation/Replacement                          September 1999                    75%
              Computer Hardware
              Core Business Software
              Desktop Software
              Embedded Systems
              Building Systems

          Contact External Trading Partners                       March 1999                   100%

          Contingency Planning                                    April 1999                    70%
</TABLE>

       To date, the Managing Partner is not aware of any significant Year 2000
issues that would cause problems in the area of safety, environmental or
business interruption. Apache will assess the risks associated with hardware,
software, infrastructure, embedded chips and external trading partners that are
not Year 2000 compliant. While Apache is confident that Year 2000 remediation
efforts will succeed in minimizing exposure to business disruption, plans are
being developed that will allow continuation of business in all but the worst
case scenarios. All remediation and replacement efforts and contingency planning
are expected to be complete by September 1999. All critical external trading
partners have been contacted to determine Year 2000 readiness and contingency
plans will be developed where assurance of Year 2000 compliance is not received
by March 31, 1999.

       In 1997, the Managing Partner initiated a project to replace existing
business software as it relates to Apache's production, land, marketing,
accounting and financial systems to more effectively and efficiently meet its
business needs. Replacement computer systems selected by the Managing Partner
from SAP America, Inc., PricewaterhouseCoopers LLP, Innovative Business
Solutions and Landmark Graphics will properly recognize dates beyond December
31, 1999. The Managing Partner plans to implement the replacement software by
March 31, 1999. The business system replacement project is 90 percent complete
and Apache believes that the March 31, 1999 deadline is attainable.



                                       9

<PAGE>   12

       The Managing Partner expects that its cost to achieve Year 2000
compliance will not exceed $4 million excluding the cost of implementing
business replacement systems. These costs will be borne by the Managing Partner
and will not have any impact on the financial results of the Partnership.

       The Managing Partner presently believes that with conversions to new
software and completion of efforts planned by the Year 2000 Task Force, the risk
associated with Year 2000 will be significantly reduced. However, the Managing
Partner is unable to assure that the consequences of Year 2000 failures of
systems maintained by Apache or by third parties will not materially adversely
impact the Partnership's results of operations, liquidity or financial
condition.

FORWARD-LOOKING STATEMENTS AND RISK

       Certain statements in this report, including statements of the future
plans, objectives, and expected performance of the Partnership, are
forward-looking statements that are dependent upon certain events, risks and
uncertainties that may be outside the Partnership's control, and which could
cause actual results to differ materially from those anticipated. Some of these
include, but are not limited to, the market prices of oil and gas, economic and
competitive conditions, inflation rates, legislative and regulatory changes,
financial market conditions, political and economic uncertainties of foreign
governments, future business decisions, and other uncertainties, all of which
are difficult to predict.

       There are numerous uncertainties inherent in estimating quantities of
proved oil and gas reserves and in projecting future rates of production and the
timing of development expenditures. The total amount or timing of actual future
production may vary significantly from reserves and production estimates. The
drilling of exploratory wells can involve significant risks, including those
related to timing, success rates and cost overruns. Lease and rig availability,
complex geology and other factors can affect these risks. Fluctuations in oil
and gas prices, or a prolonged continuation of the current low price of crude
oil, may substantially adversely affect the Partnership's financial position,
results of operations and cash flows.



                                       10

<PAGE>   13



ITEM 8. FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA

                     APACHE OFFSHORE INVESTMENT PARTNERSHIP

                          INDEX TO FINANCIAL STATEMENTS

<TABLE>
<CAPTION>
                                                                                                         PAGE
                                                                                                        NUMBER
                                                                                                        ------
<S>                                                                                                    <C>
Report of Independent Public Accountants..........................................................        12

Balance Sheet as of December 31, 1998 and 1997....................................................        13

Statement of Income for each of the three years in the period ended December 31, 1998.............        14

Statement of Cash Flows for each of the three years in the period ended December 31, 1998 ........        15

Statement of Changes in Partners' Capital for each of the three years in the period ended
    December 31, 1998.............................................................................        16

Notes to Financial Statements.....................................................................        17

Supplemental Oil and Gas Disclosures..............................................................        23
</TABLE>

Schedules -

     All financial statement schedules have been omitted because they are either
not required, not applicable or the information required to be presented is
included in the financial statements or related notes thereto.




                                       11


<PAGE>   14



                    REPORT OF INDEPENDENT PUBLIC ACCOUNTANTS




To the Partners of Apache Offshore Investment Partnership:

     We have audited the accompanying balance sheet of Apache Offshore
Investment Partnership (a Delaware partnership) as of December 31, 1998 and
1997, and the related statements of income, cash flows and changes in partners'
capital for each of the three years in the period ended December 31, 1998. These
financial statements are the responsibility of the Partnership's management. Our
responsibility is to express an opinion on these financial statements based on
our audits.

     We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to obtain
reasonable assurance about whether the financial statements are free of material
misstatement. An audit includes examining, on a test basis, evidence supporting
the amounts and disclosures in the financial statements. An audit also includes
assessing the accounting principles used and significant estimates made by
management, as well as evaluating the overall financial statement presentation.
We believe that our audits provide a reasonable basis for our opinion.

     In our opinion, the financial statements referred to above present fairly,
in all material respects, the financial position of Apache Offshore Investment
Partnership as of December 31, 1998 and 1997, and the results of its operations
and its cash flows for each of the three years in the period ended December 31,
1998, in conformity with generally accepted accounting principles.




                                             ARTHUR ANDERSEN LLP


Houston, Texas
February 26, 1999




                                       12


<PAGE>   15




                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                                  BALANCE SHEET

<TABLE>
<CAPTION>
                                                                                    DECEMBER 31,
                                                                         ----------------------------------
                                                                              1998                1997
                                                                         --------------      --------------
<S>                                                                      <C>                 <C>
                                     ASSETS

CURRENT ASSETS:
    Cash and cash equivalents                                            $    1,324,949      $      691,797
    Accrued revenues receivable                                               1,297,999           1,537,451
    Receivable from Apache Corporation                                               --             218,729
    Drilling advances                                                                --              72,020
                                                                         --------------      --------------

                                                                              2,622,948           2,519,997
                                                                         --------------      --------------

OIL AND GAS PROPERTIES, on the basis of full cost accounting:
    Proved properties                                                       168,331,700         166,397,087
    Less - Accumulated depreciation, depletion and amortization            (161,114,094)       (158,392,914)
                                                                         --------------      --------------

                                                                              7,217,606           8,004,173
                                                                         --------------      --------------

                                                                         $    9,840,554      $   10,524,170
                                                                         ==============      ==============


                        LIABILITIES AND PARTNERS' CAPITAL

CURRENT LIABILITIES:
    Accrued exploration and development                                  $      591,920      $    1,764,917
    Accrued operating expenses payable                                           98,367             112,263
    Payable to Apache Corporation                                                69,973                  --
                                                                         --------------      --------------

                                                                                760,260           1,877,180
                                                                         --------------      --------------

PARTNERS' CAPITAL:
    Managing Partner                                                            597,060             505,035
    Investing Partners (1,141.0 and 1,184.2 Units
       outstanding, respectively)                                             8,483,234           8,141,955
                                                                         --------------      --------------

                                                                              9,080,294           8,646,990
                                                                         --------------      --------------

                                                                         $    9,840,554      $   10,524,170
                                                                         ==============      ==============
</TABLE>



               The accompanying notes to financial statements are
                       an integral part of this statement.

                                       13




<PAGE>   16



                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                               STATEMENT OF INCOME

<TABLE>
<CAPTION>
                                                             FOR THE YEAR ENDED DECEMBER 31,
                                                     ----------------------------------------------
                                                         1998             1997             1996
                                                     ------------     ------------     ------------
<S>                                                  <C>              <C>              <C>
REVENUES:
    Oil and gas sales                                $  7,827,380     $ 12,066,643     $ 17,510,612
    Interest income                                        55,691           69,755           24,699
    Other income                                               --           89,249               --
                                                     ------------     ------------     ------------

                                                        7,883,071       12,225,647       17,535,311
                                                     ------------     ------------     ------------

OPERATING EXPENSES:
    Depreciation, depletion and amortization            2,721,180        2,983,020        4,320,182
    Lease operating                                     1,000,708          445,651        1,216,844
    Administrative                                        540,000          540,000          532,325
    Interest expense                                           --           12,818          339,045
                                                     ------------     ------------     ------------

                                                        4,261,888        3,981,489        6,408,396
                                                     ------------     ------------     ------------

NET INCOME                                           $  3,621,183     $  8,244,158     $ 11,126,915
                                                     ============     ============     ============

Net income allocated to:
    Managing Partner                                 $  1,061,052     $  1,967,386     $  2,651,779
    Investing Partners                                  2,560,131        6,276,772        8,475,136
                                                     ------------     ------------     ------------

                                                     $  3,621,183     $  8,244,158     $ 11,126,915
                                                     ============     ============     ============

NET INCOME PER INVESTING PARTNER UNIT                $      2,193     $      5,260     $      7,032
                                                     ============     ============     ============

WEIGHTED AVERAGE INVESTING PARTNER
    UNITS OUTSTANDING                                     1,167.4          1,193.3          1,205.3
                                                     ============     ============     ============
</TABLE>



               The accompanying notes to financial statements are
                       an integral part of this statement.


                                       14

<PAGE>   17



                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                             STATEMENT OF CASH FLOWS

<TABLE>
<CAPTION>
                                                                       FOR THE YEAR ENDED DECEMBER 31,
                                                              ------------------------------------------------
                                                                  1998              1997              1996
                                                              ------------      ------------      ------------
<S>                                                           <C>               <C>               <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
   Net income                                                 $  3,621,183      $  8,244,158      $ 11,126,915
   Adjustments to reconcile net income to net cash
     provided by operating activities:
     Depreciation, depletion and amortization                    2,721,180         2,983,020         4,320,182
     Changes in operating assets and liabilities:
       (Increase) decrease in accrued revenues receivable          239,452         1,508,734          (301,197)
       Increase (decrease) in accrued operating
         expenses payable                                          (13,896)         (286,635)          191,476
       Increase (decrease) in receivable from/payable
         to Apache Corporation                                     288,702        (1,061,813)          773,260
                                                              ------------      ------------      ------------

     Net cash provided by operating activities                   6,856,621        11,387,464        16,110,636
                                                              ------------      ------------      ------------

CASH FLOWS FROM INVESTING ACTIVITIES:
   Additions to oil and gas properties                          (2,331,287)       (4,007,934)       (1,073,490)
   Proceeds from sales of oil and gas properties                   396,674           488,750            17,425
   Non-cash portion of oil and gas property additions           (1,172,997)        1,250,969            87,018
   (Increase) decrease in drilling advances                         72,020           (72,020)            8,570
                                                              ------------      ------------      ------------

     Net cash used in investing activities                      (3,035,590)       (2,340,235)         (960,477)
                                                              ------------      ------------      ------------

CASH FLOWS FROM FINANCING ACTIVITIES:
   Repurchase of Partnership Units                                (487,313)         (179,523)         (161,899)
   Distributions to Investing Partners                          (1,731,539)       (5,362,339)       (5,411,224)
   Distributions to Managing Partner, net                         (969,027)       (2,553,540)       (2,527,170)
   Payments of long-term debt                                           --        (1,997,500)       (5,312,500)
                                                              ------------      ------------      ------------

     Net cash used in financing activities                      (3,187,879)      (10,092,902)      (13,412,793)
                                                              ------------      ------------      ------------

NET INCREASE (DECREASE) IN CASH AND CASH
   EQUIVALENTS                                                     633,152        (1,045,673)        1,737,366

CASH AND CASH EQUIVALENTS, BEGINNING
   OF YEAR                                                         691,797         1,737,470               104
                                                              ------------      ------------      ------------

CASH AND CASH EQUIVALENTS, END OF YEAR                        $  1,324,949      $    691,797      $  1,737,470
                                                              ============      ============      ============

SUPPLEMENTAL DISCLOSURES OF CASH FLOW
  INFORMATION:
   Cash paid during the year for interest                     $         --      $     11,073      $    285,000
                                                              ============      ============      ============
</TABLE>



               The accompanying notes to financial statements are
                       an integral part of this statement.

                                       15



<PAGE>   18



                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                    STATEMENT OF CHANGES IN PARTNERS' CAPITAL

<TABLE>
<CAPTION>
                                             MANAGING         INVESTING
                                             PARTNER           PARTNERS            TOTAL
                                           ------------      ------------      ------------

<S>                                        <C>               <C>               <C>
BALANCE, DECEMBER 31, 1995                 $    966,580      $  4,505,032      $  5,471,612

  Distributions, net                         (2,527,170)       (5,411,224)       (7,938,394)

  Repurchase of Partnership Units                    --          (161,899)         (161,899)

  Net income                                  2,651,779         8,475,136        11,126,915
                                           ------------      ------------      ------------

BALANCE, DECEMBER 31, 1996                    1,091,189         7,407,045         8,498,234

  Distributions, net                         (2,553,540)       (5,362,339)       (7,915,879)

  Repurchase of Partnership Units                    --          (179,523)         (179,523)

  Net income                                  1,967,386         6,276,772         8,244,158
                                           ------------      ------------      ------------

BALANCE, DECEMBER 31, 1997                      505,035         8,141,955         8,646,990

  Distributions, net                           (969,027)       (1,731,539)       (2,700,566)

  Repurchase of Partnership Units                    --          (487,313)         (487,313)

  Net income                                  1,061,052         2,560,131         3,621,183
                                           ------------      ------------      ------------

BALANCE, DECEMBER 31, 1998                 $    597,060      $  8,483,234      $  9,080,294
                                           ============      ============      ============
</TABLE>



               The accompanying notes to financial statements are
                       an integral part of this statement.


                                       16


<PAGE>   19


                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                          NOTES TO FINANCIAL STATEMENTS


(1)  ORGANIZATION

     NATURE OF OPERATIONS -

         Apache Offshore Investment Partnership was formed as a Delaware general
     partnership on October 31, 1983, consisting of Apache Corporation (Apache)
     as Managing Partner and public investors as Investing Partners. The general
     partnership invested its entire capital in Apache Offshore Petroleum
     Limited Partnership, a Delaware limited partnership formed to conduct oil
     and gas exploration, development and production operations. The
     accompanying financial statements include the accounts of both the limited
     and general partnerships. Apache is the general partner of both the limited
     and general partnerships, and holds approximately five percent of the
     1,141.0 Investing Partner Units (Units) outstanding at December 31, 1998.
     The term "Partnership", as used hereafter, refers to the limited or the
     general partnership, as the case may be.

         The Partnership purchased, at cost, an 85 percent interest in offshore
     leasehold interests acquired by Apache as a co-venturer in a series of oil
     and gas exploration, development and production activities on 87 federal
     lease tracts (12 remain as of December 31, 1998) in the Gulf of Mexico,
     offshore Louisiana and Texas. The remaining 15 percent interest was
     purchased by an affiliated partnership or retained by Apache. The
     Partnership acquired an increased net revenue interest in Matagorda Island
     Blocks 681 and 682 in November 1992, when the Partnership and Apache formed
     a joint venture to acquire a 92.6 percent working interest in the blocks.

         Since inception, the Partnership has participated in 14 federal
     offshore lease sales in which 49 prospects were acquired (through the same
     date 42 of those prospects have been surrendered/sold). The Partnership's
     working interests in the seven remaining venture prospects range from 6.29
     percent to 9.44 percent.

         The Partnership's future financial condition and results of operations
     will depend largely upon prices received for its oil and natural gas
     production and the costs of acquiring, finding, developing and producing
     reserves. A substantial portion of the Partnership's production is sold
     under market-sensitive contracts. Prices for oil and natural gas are
     subject to fluctuations in response to changes in supply, market
     uncertainty and a variety of factors beyond the Partnership's control.
     These factors include worldwide political instability (especially in the
     Middle East), the foreign supply of oil and natural gas, the price of
     foreign imports, the level of consumer demand, and the price and
     availability of alternative fuels. With natural gas accounting for 83
     percent of the Partnership's 1998 production and 67 percent of total proved
     reserves, on an energy equivalent basis, the Partnership is affected more
     by fluctuations in natural gas prices than in oil prices.

         Under the terms of the Partnership Agreements, the Investing Partners
     receive 80 percent and Apache receives 20 percent of revenue. The Investing
     Partners generally pay for 90 percent and Apache generally pays for 10
     percent of exploration and development costs and expenses incurred by the
     Partnership. However, intangible drilling costs, interest costs and fees or
     expenses related to the loans incurred by the Partnership are allocated 99
     percent to the Investing Partners and one percent to Apache until such time
     as the amount so allocated to the Investing Partners equals 90 percent of
     the total amount of such costs, including such costs incurred by Apache
     prior to the formation of the Partnerships.



                                       17

<PAGE>   20



                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                   NOTES TO FINANCIAL STATEMENTS - (CONTINUED)

     RIGHT OF PRESENTMENT -

         An amendment to the Partnership Agreement adopted in February 1994,
     created a right of presentment under which all Investing Partners have a
     limited and voluntary right to offer their Units to the Partnership twice
     each year to be purchased for cash. During 1998, the Investing Partners
     sold a total of 43.22 Units to the Partnership for a total of approximately
     $487,000 in cash. The first right of presentment was based upon a valuation
     date of December 31, 1997 for a purchase price of $11,161 per Unit, plus
     interest to the date of payment. The second presentment offer was based on
     a valuation date of June 30, 1998 for a purchase price of $9,824 per Unit,
     plus interest to the payment date. During 1997 and 1996, the Partnership
     paid the Investing Partners approximately $180,000 and $162,000,
     respectively, to acquire a total of 28.16 Units.

         The Partnership is not in a position to predict how many Units will be
     presented for repurchase during 1999, however, no more than 10 percent of
     the outstanding Units may be purchased under the right of presentment in
     any year. The Partnership has no obligation to purchase any Units presented
     to the extent that it determines that it has insufficient funds for such
     purchases.

         The table below sets forth the total repurchase price and the
     repurchase price per Unit for all outstanding Units at each presentment
     period, based on the right of presentment valuation formula defined in the
     amendment to the Partnership Agreement. The right of presentment offers,
     made twice annually, are based on a discounted Unit value formula. The
     discounted Unit value will be not less than the Investing Partner's share
     of: (a) the sum of (i) 70 percent of the discounted estimated future net
     revenues from proved reserves, discounted at a rate of 1.5 percent over
     prime or First National Bank of Chicago's base rate in effect at the time
     the calculation is made, (ii) cash on hand, (iii) prepaid expenses, (iv)
     accounts receivable less a reasonable reserve for doubtful accounts, (v)
     oil and gas properties other than proved reserves at cost less any amounts
     attributable to drilling and completion costs incurred by the Partnership
     and included therein, and (vi) the book value of all other assets of the
     Partnership, less the debts, obligations and other liabilities of all kinds
     (including accrued expenses) then allocable to such interest in the
     Partnership, all determined as of the valuation date, divided by (b) the
     number of Units, and fractions thereof, outstanding as of the valuation
     date. The discounted Unit value does not purport to be, and may be
     substantially different from, the fair market value of a Unit.

<TABLE>
<CAPTION>
                   RIGHT OF PRESENTMENT                  TOTAL REPURCHASE                REPURCHASE PRICE
                      VALUATION DATE                          PRICE                          PER UNIT
                 -------------------------              -------------------             --------------------
<S>             <C>                                    <C>                             <C>
                 December 31, 1995                      $       14,181,413              $            10,698
                 June 30, 1996                                  16,881,655                           10,572
                 December 31, 1996                              17,514,216                           13,621
                 June 30, 1997                                  17,188,997                           10,946
                 December 31, 1997                              13,216,700                           11,161
                 June 30, 1998                                  13,072,171                            9,824
</TABLE>

     CAPITAL CONTRIBUTIONS -

         A total of $85,000 per Unit, or approximately 57 percent of investor
     subscriptions, were called through December 31, 1998. The Partnership
     determined the full purchase price of $150,000 per Unit was not needed, and
     upon completion of the last subscription call in November 1989, released
     the Investing Partners from their remaining liability. As a result of
     investors defaulting on cash calls and repurchases under the presentment
     offer discussed above, the original 1,500 Units have been reduced to
     1,141.0 Units at December 31, 1998.



                                       18


<PAGE>   21



                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                   NOTES TO FINANCIAL STATEMENTS - (CONTINUED)


(2)  SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

     STATEMENT PRESENTATION -

         The accounts of the Partnership are maintained on a tax basis method of
     accounting in accordance with the Articles of Partnership and methods of
     reporting allowed for federal income tax purposes.

         Financial statements included in reports that the Partnership files
     with the Securities and Exchange Commission (SEC) are required to be
     prepared in conformity with generally accepted accounting principles.
     Accordingly, the accompanying financial statements were prepared to reflect
     memorandum entries to convert from tax basis to the accrual basis method in
     conformity with generally accepted accounting principles.

     CASH EQUIVALENTS -

         The Partnership considers all highly liquid debt instruments purchased
     with an original maturity of three months or less to be cash equivalents.
     These investments are carried at cost which approximates market.

     OIL AND GAS PROPERTIES -

         The Partnership uses the full cost method of accounting for financial
     statement purposes. Under this method, the Partnership capitalizes all
     acquisition, exploration and development costs incurred for the purpose of
     finding oil and gas reserves. The amounts capitalized under this method
     include dry hole costs, leasehold costs, engineering, geological,
     exploration, development and other similar costs. Costs associated with
     production and administrative functions are expensed in the period
     incurred. Unless a significant portion of the Partnership's reserve volumes
     are sold (greater than 25 percent), proceeds from the sale of oil and gas
     properties are accounted for as reductions to capitalized costs, and gains
     or losses are not recognized.

         Capitalized costs of oil and gas properties are amortized on the future
     gross revenue method whereby depreciation, depletion and amortization
     (DD&A) expense is computed quarterly by dividing current period oil and gas
     sales by estimated future gross revenue from proved oil and gas reserves
     (including current period oil and gas sales) and applying the resulting
     rate to the net cost of evaluated oil and gas properties, including
     estimated future development costs. The amortizable base includes estimated
     dismantlement, restoration and abandonment costs, net of estimated salvage
     values.

         The Partnership limits the capitalized costs of proved oil and gas
     properties, net of accumulated DD&A, to the estimated future net cash flows
     from proved oil and gas reserves discounted at 10 percent, plus the lower
     of cost or fair value of unproved properties included in the costs being
     amortized, if any. If capitalized costs exceed this limit, the excess is
     charged to DD&A expense. The Partnership has not recorded any write-downs
     of capitalized costs for the three years presented.

     REVENUE RECOGNITION -

         The Partnership uses the sales method of accounting for natural gas
     revenues. Under this method, revenues are recognized based on actual
     volumes of gas sold to purchasers. The volumes of gas sold may differ from
     the volumes to which the Partnership is entitled based on its interests in
     the properties. Revenue is deferred and a liability is recorded for those
     properties where the estimated remaining reserves will not be sufficient to
     enable the underproduced owner to recoup its entitled share through
     production.

     PER UNIT CALCULATION -

         The net income per Investing Partner Unit is calculated by dividing the
     aggregate Investing Partners' net income for the period by the number of
     weighted average Investing Partner Units outstanding for that period.



                                       19

<PAGE>   22
                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                   NOTES TO FINANCIAL STATEMENTS - (CONTINUED)


     INCOME TAXES -

         The profit or loss of the Partnership for federal income tax reporting
     purposes is included in the income tax returns of the partners.
     Accordingly, no recognition has been given to income taxes in the
     accompanying financial statements.

     USE OF ESTIMATES -

         The preparation of financial statements in conformity with generally
     accepted accounting principles requires management to make estimates and
     assumptions that affect the reported amounts of assets and liabilities and
     disclosure of contingent assets and liabilities at the date of the
     financial statements and the reported amounts of revenues and expenses
     during the reporting period. Actual results could differ from those
     estimates. Significant estimates with regard to these financial statements
     include the estimate of proved oil and gas reserve quantities and the
     related present value of estimated future net cash flows therefrom. See
     "Supplemental Oil and Gas Disclosures" below.

     PAYABLE TO/RECEIVABLE FROM APACHE -

         Payable to/receivable from Apache represents the net result of the
     Investing Partners' revenue and expenditure transactions in the current
     month. Generally, this amount will be transferred to or funded by Apache,
     as appropriate, in the month after the Partnership's transactions are
     processed and the net results from operations are determined.

     MAINTENANCE AND REPAIRS -

         Maintenance and repairs are charged to expense as incurred.
     Recompletions and replacements that improve or extend the life of existing
     properties are capitalized.


(3)  COMPENSATION TO APACHE

         Apache is entitled to the following types of compensation and
reimbursement for costs and expenses.

<TABLE>
<CAPTION>
                                                                                   TOTAL REIMBURSED BY THE INVESTING
                                                                                 PARTNERS FOR THE YEAR ENDED DECEMBER 31,
                                                                                 ----------------------------------------
                                                                                      1998         1997         1996
                                                                                    --------     --------     --------
                                                                                              (In thousands)
<S>                                                                                 <C>          <C>          <C>
        a. Apache is reimbursed for general, administrative and
           overhead expenses incurred in connection with the
           management and operation of the Partnership's business                   $    432     $    432     $    426
                                                                                    ========     ========     ========

        b. Apache is reimbursed for exploration and development overhead costs
           incurred in the Partnership's operations. These costs are based on
           exploration and development activities and are capitalized to oil 
           and gas properties                                                       $    140     $    222     $     77
                                                                                    ========     ========     ========
</TABLE>
         Apache operates certain Partnership properties. Billings to the
     Partnership are made on the same basis as to unaffiliated third parties or
     at prevailing industry rates.



                                       20

<PAGE>   23



                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                   NOTES TO FINANCIAL STATEMENTS - (CONTINUED)


(4)      OIL AND GAS PROPERTIES

         The following tables contain direct cost information and changes in the
     Partnership's oil and gas properties for each of the years ended December
     31. All costs of oil and gas properties are currently being amortized.

<TABLE>
<CAPTION>
                                                                    1998            1997            1996
                                                                 ----------      ----------      ----------
                                                                              (In thousands)
<S>                                                             <C>             <C>              <C>
        Oil and Gas Properties
        ----------------------

        Balance, beginning of year                               $  166,397      $  162,878      $  161,822
        Costs incurred during the year:
          Leasehold additions -
             Investing Partners                                          17               5              23
             Managing Partner                                             2               1               3
          Development -
             Investing Partners                                       2,257           3,906           1,020
             Managing Partner                                            56              96              27
          Property sales proceeds (1) -
             Investing Partners                                        (357)           (440)            (13)
             Managing Partner                                           (40)            (49)             (4)
                                                                 ----------      ----------      ----------

        Balance, end of year                                     $  168,332      $  166,397      $  162,878
                                                                 ==========      ==========      ==========
</TABLE>

(1)      The 1998 property sales proceeds are a result of the sale of the
         Krypton Prospect (West Cameron Block 368). The 1997 property sales
         proceeds are a result of the sale of the Glenda Prospect (High Island
         Block A-6) and the sale of the Partnership's interest in a farmout on
         the Roberto Prospect (Matagorda Island Block 670/682). The 1996
         property sales proceeds are a result of the sale of the No-See-Um
         Prospect (Vermillion Block 226/337).

<TABLE>
<CAPTION>
                                                                  MANAGING      INVESTING
                                                                  PARTNER        PARTNERS         TOTAL
                                                                 ----------     ----------     ----------
                                                                              (In thousands)
<S>                                                              <C>            <C>            <C>
        Accumulated Depreciation, Depletion and Amortization
        ----------------------------------------------------

        Balance, December 31, 1995                               $   19,173     $  131,917     $  151,090
          Provision                                                     467          3,853          4,320
                                                                 ----------     ----------     ----------

        Balance, December 31, 1996                                   19,640        135,770        155,410
          Provision                                                     265          2,718          2,983
                                                                 ----------     ----------     ----------

        Balance, December 31, 1997                                   19,905        138,488        158,393
          Provision                                                     196          2,525          2,721
                                                                 ----------     ----------     ----------

        Balance, December 31, 1998                               $   20,101     $  141,013     $  161,114
                                                                 ==========     ==========     ==========
</TABLE>

          The Partnership's aggregate DD&A expense was 35 percent of oil and gas
     sales for 1998 and 25 percent for both 1997 and 1996.




                                       21

<PAGE>   24



                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                   NOTES TO FINANCIAL STATEMENTS - (CONTINUED)


(5)  MAJOR CUSTOMER INFORMATION

         Revenues received from major third party customers that exceeded 10
     percent of oil and gas sales are discussed below. No other third party
     customers individually accounted for more than ten percent of oil and gas
     sales.

         Beginning in April 1996, Producers Energy Marketing LLC (ProEnergy), an
     affiliate of Apache until June 1998, became the principal purchaser of the
     Partnership's natural gas production. Sales to ProEnergy accounted for 92
     percent, 87 percent, and 73 percent of the Partnership's oil and gas sales
     in 1998, 1997 and 1996, respectively. In June 1998, Apache formed a
     strategic alliance with Cinergy Corp. (Cinergy) to market substantially all
     of Apache's natural gas production from North America and sold its 57
     percent interest in ProEnergy to Cinergy. ProEnergy will continue to market
     Apache's North American natural gas production for 10 years, with an option
     to terminate after six years, under an amended and restated gas purchase
     agreement effective July 1, 1998. The prices the Partnership received for
     its gas production prior to the sale of ProEnergy were, in the opinion of
     Apache, comparable to the prices that would have been received from a
     non-affiliated party. The prices the Partnership received after the sale of
     ProEnergy and will continue to receive for its gas production, in the
     opinion of Apache, approximate market prices.

         Sales of oil and condensate to Plains Petroleum Operating Co. accounted
     for five percent, nine percent, and 10 percent of the Partnership's oil and
     gas sales in 1998, 1997 and 1996, respectively.

         Effective November 1992, with Apache's and the Partnership's
     acquisition of an additional net revenue interest in Matagorda Island
     Blocks 681 and 682, a wholly-owned subsidiary of Apache purchased from
     Shell Oil Company (Shell) a 14.4 mile natural gas and condensate pipeline
     connecting Matagorda Island Block 681 to onshore markets. The Partnership
     paid the Apache subsidiary transportation fees totaling $.1 million in 1998
     and $.2 million in each of 1997 and 1996 for the Partnership's share of
     gas. The fees, which are netted against oil and gas sales on the income
     statement, were at the same rates and terms as previously paid to Shell.

         The Partnership's revenues are derived principally from
     uncollateralized sales to customers in the oil and gas industry; therefore,
     customers may be similarly affected by changes in economic and other
     conditions within the industry. The Partnership has not experienced
     material credit losses on such sales.


(6)  DEBT

         In July 1992, through Apache, the Partnership obtained a line of
     credit. Proceeds from this revolving bank facility were used to repay a
     limited recourse note which had previously been issued to finance offshore
     leasehold in the Partnership. The $2.0 million of outstanding debt at
     December 31, 1996, was due in 1998; however, on January 31, 1997, the
     Partnership repaid the loan in its entirety and terminated the facility.

         It is expected that cash flows from operating activities will be
     sufficient to meet the Partnership's liquidity needs for routine operations
     over the next two years. However, in the event future short-term operating
     cash requirements are greater than the Partnership's financial resources,
     the Partnership will seek short-term, interest-bearing advances from the
     Managing Partner as needed.


(7)  FINANCIAL INSTRUMENTS

         The carrying amount of cash and cash equivalents, accrued revenue
     receivables and other financial instruments included in the accompanying
     balance sheet approximated their fair values at December 31, 1998 and 1997.
     The Partnership did not engage in hedging activities during the three-year
     period ended December 31, 1998.



                                       22

<PAGE>   25

                      SUPPLEMENTAL OIL AND GAS DISCLOSURES
                                   (UNAUDITED)


     OIL AND GAS RESERVE INFORMATION -

         Proved oil and gas reserve quantities are based on estimates prepared
     by Ryder Scott Company Petroleum Engineers, independent petroleum
     engineers, in accordance with guidelines established by the SEC. These
     reserves are subject to revision due to the inherent imprecision in
     estimating reserves, and are revised as additional information becomes
     available. All the Partnership's reserves are located offshore Texas and
     Louisiana.

         There are numerous uncertainties inherent in estimating quantities of
     proved reserves and projecting future rates of production and timing of
     development expenditures. The following reserve data represents estimates
     only and should not be construed as being exact.

     (Oil in Mbbls and gas in MMcf)

<TABLE>
<CAPTION>
                                                            1998                     1997                       1996
                                                    --------------------      --------------------      --------------------
                                                      OIL          GAS          OIL          GAS          OIL          GAS
                                                    -------      -------      -------      -------      -------      -------
<S>                                                 <C>          <C>          <C>          <C>          <C>          <C>   
Proved Reserves
---------------

  Beginning of year                                     922       12,511        1,065       16,396        1,169       20,848
    Extensions, discoveries and other additions           3        2,080           92          289           --          252
    Revisions of previous estimates                      17         (997)         281         (150)          60          957
    Production                                         (106)      (3,127)        (125)      (3,878)        (164)      (5,651)
    Sales of reserves in-place                           (4)        (198)        (391)        (146)          --          (10)
                                                    -------      -------      -------      -------      -------      -------

  End of year                                           832       10,269          922       12,511        1,065       16,396
                                                    =======      =======      =======      =======      =======      =======

Proved Developed
----------------

  Beginning of year                                     883       10,824          917       14,223        1,112       18,798
                                                    =======      =======      =======      =======      =======      =======

  End of year                                           792        8,585          883       10,824          917       14,223
                                                    =======      =======      =======      =======      =======      =======
</TABLE>


                                       23

<PAGE>   26



               SUPPLEMENTAL OIL AND GAS DISCLOSURES - (CONTINUED)
                                   (UNAUDITED)


     FUTURE NET CASH FLOWS -

         The following table sets forth unaudited information concerning future
     net cash flows from proved oil and gas reserves. Future cash inflows are
     based on year-end prices. Operating costs and future development costs are
     based on current costs with no escalation. As the Partnership pays no
     income taxes, estimated future income tax expenses are omitted. This
     information does not purport to present the fair value of the Partnership's
     oil and gas assets, but does present a standardized disclosure concerning
     possible future net cash flows that would result under the assumptions
     used.

     Discounted Future Net Cash Flows Relating to Proved Reserves
     ------------------------------------------------------------
<TABLE>
<CAPTION>
                                                                     DECEMBER 31,
                                                        ------------------------------------
                                                          1998          1997          1996
                                                        --------      --------      --------
                                                                   (In thousands)
<S>                                                     <C>          <C>            <C>
        Future cash inflows                             $ 27,473      $ 46,733      $ 97,475
        Future production and development costs           (8,744)      (10,739)      (14,072)
                                                        --------      --------      --------

        Net cash flows                                    18,729        35,994        83,403
        10 percent annual discount rate                   (5,001)       (9,137)      (21,325)
                                                        --------      --------      --------

        Discounted future net cash flows                $ 13,728      $ 26,857      $ 62,078
                                                        ========      ========      ========
</TABLE>

          The following table sets forth the principal sources of change in the
     discounted future net cash flows:

<TABLE>
<CAPTION>
                                                           FOR THE YEAR ENDED DECEMBER 31,
                                                        ------------------------------------
                                                          1998          1997          1996
                                                        --------      --------      --------
                                                                   (In thousands)

<S>                                                    <C>           <C>           <C>
        Sales, net of production costs                  $ (6,827)     $(11,621)     $(16,294)
        Net change in prices and production costs         (9,548)      (31,310)       22,269
        Extensions, discoveries and other additions        2,662         1,751           862
        Development costs incurred                         1,278            --            --
        Revisions of quantities                           (1,029)        2,616         3,920
        Accretion of discount                              2,686         6,208         4,912
        Changes in future development costs                 (132)          617          (607)
        Sales of reserves in-place                          (192)         (468)          (18)
        Changes in production rates and other             (2,027)       (3,014)       (2,081)
                                                        --------      --------      --------

                                                        $(13,129)     $(35,221)     $ 12,963
                                                        ========      ========      ========
</TABLE>



                                       24

<PAGE>   27



ITEM 9.  CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON ACCOUNTING AND
         FINANCIAL DISCLOSURE

     None.



                                    PART III


ITEM 10. DIRECTORS AND EXECUTIVE OFFICERS OF THE PARTNERSHIP

     All management functions are performed by Apache, the Managing Partner of
the Partnership. The Partnership itself has no officers or directors.
Information concerning the officers and directors of Apache set forth under the
captions "Nominees for Election as Directors", "Continuing Directors",
"Executive Officers of the Company", and "Voting Securities and Principal
Holders" in the proxy statement relating to the 1999 annual meeting of
shareholders of Apache (the Apache Proxy) is incorporated herein by reference.


ITEM 11. EXECUTIVE COMPENSATION

     See Note (3), "Compensation to Apache" of the Partnership's financial
statements, under Item 8 above, for information regarding compensation to Apache
as Managing Partner. The information concerning the compensation paid by Apache
to its officers and directors set forth under the captions "Summary Compensation
Table", "Option/SAR Grants Table", "Option/SAR Exercises and Year-End Value
Table", "Employment Contracts and Termination of Employment and
Change-in-Control Arrangements", and "Director Compensation" in the Apache Proxy
is incorporated herein by reference.


ITEM 12. SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT

     Apache, as an Investing Partner and the General Partner, owns 53 Units, or
4.6 percent of the outstanding Units of the Partnership, as of December 31,
1998. Directors and officers of Apache own 9.7 Units, slightly less than one
percent of the Partnership's Units, as of December 31, 1998. Apache owns a
one-percent General Partner interest (15 equivalent Units). To the knowledge of
the Partnership, no Investing Partner owns, of record or beneficially, more than
five percent of the Partnership's outstanding Units.


ITEM 13. CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS

     Effective November 1992, with Apache's and the Partnership's acquisition of
an additional net revenue interest in Matagorda Island Blocks 681 and 682, a
wholly-owned subsidiary of Apache purchased from Shell a 14.4 mile-long natural
gas and condensate pipeline connecting Matagorda Island Block 681 to onshore
markets. The Partnership paid the Apache subsidiary transportation fees totaling
$.1 million in 1998 and $.2 million in each of 1997 and 1996 for Partnership's
share of gas. The fees, which are netted against oil and gas sales on the income
statement, were at the same rates and terms as previously paid to Shell.

     Apache markets the Partnership's natural gas production through ProEnergy.
In June 1998, Apache formed a strategic alliance with Cinergy to market
substantially all of Apache's natural gas production from North America and sold
its 57 percent interest in ProEnergy to Cinergy. ProEnergy will continue to
market Apache's North American natural gas production for 10 years, with an
option to terminate after six years, under an amended and restated gas purchase
agreement effective July 1, 1998. The prices the Partnership received for its
gas production prior to the sale of ProEnergy were, in the opinion of Apache,
comparable to the prices that would have been received from a non-affiliated
party. The prices the Partnership received after the sale of ProEnergy and will
continue to receive for its gas production, in the opinion of Apache,
approximate market prices.



                                       25

<PAGE>   28
                                     PART IV


ITEM 14. EXHIBITS, FINANCIAL STATEMENT SCHEDULES, AND REPORTS ON FORM 8-K

 a. (1)  Financial Statements - See accompanying index to financial statements
         in Item 8 above.

    (2)  Financial Statement Schedules - See accompanying index to financial
         statements in Item 8 above.

    (3)  Exhibits

              3.1   Partnership Agreement of Apache Offshore Investment
                    Partnership (incorporated by reference to Exhibit (3)(i) to
                    Form 10 filed by Partnership with the Commission on April
                    30, 1985, Commission File No. 0-13546).

              3.2   Amendment No. 1, dated February 11, 1994, to the Partnership
                    Agreement of Apache Offshore Investment Partnership
                    (incorporated by reference to Exhibit 3.3 to Partnership's
                    Annual Report on Form 10-K for the year ended December 31,
                    1993, Commission File No. 0-13546).

              3.3   Limited Partnership Agreement of Apache Offshore Petroleum
                    Limited Partnership (incorporated by reference to Exhibit
                    (3)(ii) to Form 10 filed by Partnership with the Commission
                    on April 30, 1985, Commission File No. 0-13546).

             10.1   Credit Agreement dated July 24, 1992, between Apache, the
                    Lenders named therein and the First National Bank of
                    Chicago, as Agent (incorporated by reference to Exhibit 10.1
                    to Partnership's Quarterly Report on Form 10-Q for the
                    quarter ended June 30, 1992, Commission File No. 0-13546).

             10.2   Second Amendment, dated as of July 29, 1994, to Credit
                    Agreement between Apache, the Lenders named therein and the
                    First National Bank of Chicago, as Agent (incorporated by
                    reference to Exhibit 10.1 to Partnership's Quarterly Report
                    on Form 10-Q for the quarter ended September 30, 1994,
                    Commission File No. 0-13546).

             10.3   Third Amendment, dated as of March 31, 1995, to the Credit
                    Agreement between Apache, the Lenders named therein and the
                    First National Bank of Chicago, as Agent (incorporated by
                    reference to Exhibit 10.6 to Partnership's Annual Report on
                    Form 10-K for the year ended December 31, 1995, Commission
                    File No. 0-13546).

             10.4   Form of Assignment and Assumption Agreement between Apache
                    Corporation and Apache Offshore Petroleum Limited
                    Partnership (incorporated by reference to Exhibit 10.2 to
                    Partnership's Quarterly Report on Form 10-Q for the quarter
                    ended June 30, 1992, Commission File No. 0-13546).

             10.5   Joint Venture Agreement, dated as of November 23, 1992,
                    between Apache Corporation and Apache Offshore Petroleum
                    Limited Partnership (incorporated by reference to Exhibit
                    10.6 to Partnership's Annual Report on Form 10-K for the
                    year ended December 31, 1992, Commission File No. 0-13546).

             10.6   Matagorda Island 681 Field Purchase and Sale Agreement with
                    Option to Exchange, dated November 24, 1992, between Apache
                    Corporation, Shell Offshore, Inc. and SOI Royalties, Inc.
                    (incorporated by reference to Exhibit 10.7 to Partnership's
                    Annual Report on Form 10-K for the year ended December 31,
                    1992, Commission File No. 0-13546).

            *23.1   Consent of Ryder Scott Company Petroleum Engineers.

            *27.1   Financial Data Schedule.



                                       26

<PAGE>   29

             99.1   Consent statement of the Partnership, dated January 7, 1994
                    (incorporated by reference to Exhibit 99.1 to Partnership's
                    Annual Report on Form 10-K for the year ended December 31,
                    1993, Commission File No. 0-13546).

             99.2   Proxy statement to be dated on or about March 30, 1999,
                    relating to the 1999 annual meeting of shareholders of
                    Apache Corporation (incorporated by reference to the
                    document filed by Apache pursuant to Rule 14A, Commission
                    File No. 1-4300).

                    *Filed herewith.

     b.   Reports filed on Form 8-K.

          No reports on Form 8-K were filed during the fiscal quarter ended
     December 31, 1998.






                                       27

<PAGE>   30


                                   SIGNATURES

     Pursuant to the requirements of Section 13 or 15(d) of the Securities
Exchange Act of 1934, the Partnership has duly caused this report to be signed
on its behalf by the undersigned, thereunto duly authorized.

                                  APACHE OFFSHORE INVESTMENT PARTNERSHIP

                                  By:  Apache Corporation, General Partner


Date:   March 15, 1999            By:  /s/ Raymond Plank
                                       ----------------------------------------
                                       Raymond Plank,
                                       Chairman and Chief Executive Officer


                                POWER OF ATTORNEY

     The officers and directors of Apache Corporation, General Partner of Apache
Offshore Investment Partnership, whose signatures appear below, hereby
constitute and appoint Raymond Plank, G. Steven Farris, Z.S. Kobiashvili and
Roger B. Plank, and each of them (with full power to each of them to act alone),
the true and lawful attorney-in-fact to sign and execute, on behalf of the
undersigned, any amendment(s) to this report and each of the undersigned does
hereby ratify and confirm all that said attorneys shall do or cause to be done
by virtue thereof.

     Pursuant to the requirements of the Securities Exchange Act of 1934, this
report has been signed below by the following persons on behalf of the
Partnership and in the capacities and on the dates indicated.

<TABLE>
<CAPTION>
                  SIGNATURE                                            TITLE                                DATE
----------------------------------------------         ----------------------------------------      -------------------
<S>                                                    <C>                                           <C>
/s/ Raymond Plank                                      Chairman and Chief Executive                    March 15, 1999
--------------------------------------------             Officer (Principal Executive Officer)
Raymond Plank                                            


/s/Roger B. Plank                                      Vice President and Chief Financial              March 15, 1999
--------------------------------------------             Officer (Principal Financial Officer)
Roger B. Plank


/s/ Thomas L. Mitchell                                 Vice President and Controller                   March 15, 1999
--------------------------------------------             (Principal Accounting Officer)
Thomas L. Mitchell
</TABLE>





<PAGE>   31

<TABLE>
<CAPTION>
                  SIGNATURE                                            TITLE                                DATE
----------------------------------------------         --------------------------------------        -------------------
<S>                                                    <C>                                           <C>

/s/ Frederick M. Bohen                                 Director                                        March 15, 1999
--------------------------------------------
Frederick M. Bohen


/s/ G. Steven Farris                                   Director                                        March 15, 1999
--------------------------------------------
G. Steven Farris


/s/Randolph M. Ferlic                                  Director                                        March 15, 1999
--------------------------------------------
Randolph M. Ferlic


/s/ Eugene C. Fiedorek                                 Director                                        March 15, 1999
--------------------------------------------
Eugene C. Fiedorek


/s/ A. D. Frazier, Jr.                                 Director                                        March 15, 1999
--------------------------------------------
A. D. Frazier, Jr.


/s/ Stanley K. Hathaway                                Director                                        March 15, 1999
--------------------------------------------
Stanley K. Hathaway


/s/ John A. Kocur                                      Director                                        March 15, 1999
--------------------------------------------
John A. Kocur


/s/ George D. Lawrence Jr.                             Director                                        March 15, 1999
--------------------------------------------
George D. Lawrence Jr.


/s/ Mary Ralph Lowe                                    Director                                        March 15, 1999
--------------------------------------------
Mary Ralph Lowe


/s/ F. H. Merelli                                      Director                                        March 15, 1999
--------------------------------------------
F. H. Merelli


/s/ Joseph A. Rice                                     Director                                        March 15, 1999
--------------------------------------------
Joseph A. Rice
</TABLE>


<PAGE>   32

                               INDEX TO EXHIBITS
<TABLE>
<CAPTION>
    Exhibit
    Number                            Description
    ------                            -----------

<S>                 <C>
     3.1            Partnership Agreement of Apache Offshore Investment
                    Partnership (incorporated by reference to Exhibit (3)(i) to
                    Form 10 filed by Partnership with the Commission on April
                    30, 1985, Commission File No. 0-13546).

     3.2            Amendment No. 1, dated February 11, 1994, to the Partnership
                    Agreement of Apache Offshore Investment Partnership
                    (incorporated by reference to Exhibit 3.3 to Partnership's
                    Annual Report on Form 10-K for the year ended December 31,
                    1993, Commission File No. 0-13546).

     3.3            Limited Partnership Agreement of Apache Offshore Petroleum
                    Limited Partnership (incorporated by reference to Exhibit
                    (3)(ii) to Form 10 filed by Partnership with the Commission
                    on April 30, 1985, Commission File No. 0-13546).

     10.1           Credit Agreement dated July 24, 1992, between Apache, the
                    Lenders named therein and the First National Bank of
                    Chicago, as Agent (incorporated by reference to Exhibit 10.1
                    to Partnership's Quarterly Report on Form 10-Q for the
                    quarter ended June 30, 1992, Commission File No. 0-13546).

     10.2           Second Amendment, dated as of July 29, 1994, to Credit
                    Agreement between Apache, the Lenders named therein and the
                    First National Bank of Chicago, as Agent (incorporated by
                    reference to Exhibit 10.1 to Partnership's Quarterly Report
                    on Form 10-Q for the quarter ended September 30, 1994,
                    Commission File No. 0-13546).

     10.3           Third Amendment, dated as of March 31, 1995, to the Credit
                    Agreement between Apache, the Lenders named therein and the
                    First National Bank of Chicago, as Agent (incorporated by
                    reference to Exhibit 10.6 to Partnership's Annual Report on
                    Form 10-K for the year ended December 31, 1995, Commission
                    File No. 0-13546).

     10.4           Form of Assignment and Assumption Agreement between Apache
                    Corporation and Apache Offshore Petroleum Limited
                    Partnership (incorporated by reference to Exhibit 10.2 to
                    Partnership's Quarterly Report on Form 10-Q for the quarter
                    ended June 30, 1992, Commission File No. 0-13546).

     10.5           Joint Venture Agreement, dated as of November 23, 1992,
                    between Apache Corporation and Apache Offshore Petroleum
                    Limited Partnership (incorporated by reference to Exhibit
                    10.6 to Partnership's Annual Report on Form 10-K for the
                    year ended December 31, 1992, Commission File No. 0-13546).

     10.6           Matagorda Island 681 Field Purchase and Sale Agreement with
                    Option to Exchange, dated November 24, 1992, between Apache
                    Corporation, Shell Offshore, Inc. and SOI Royalties, Inc.
                    (incorporated by reference to Exhibit 10.7 to Partnership's
                    Annual Report on Form 10-K for the year ended December 31,
                    1992, Commission File No. 0-13546).

     *23.1          Consent of Ryder Scott Company Petroleum Engineers.

     *27.1          Financial Data Schedule.

     99.1           Consent statement of the Partnership, dated January 7, 1994
                    (incorporated by reference to Exhibit 99.1 to Partnership's
                    Annual Report on Form 10-K for the year ended December 31,
                    1993, Commission File No. 0-13546).

     99.2           Proxy statement to be dated on or about March 30, 1999,
                    relating to the 1999 annual meeting of shareholders of
                    Apache Corporation (incorporated by reference to the
                    document filed by Apache pursuant to Rule 14A, Commission
                    File No. 1-4300).

                    *Filed herewith.

</TABLE>