<PAGE>   1

                       SECURITIES AND EXCHANGE COMMISSION

                             WASHINGTON, D.C. 20549

                                    FORM 10-Q



          [X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934


                  For the Quarterly Period Ended June 30, 1999

                                       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
                     --------------------------------------
             (Exact Name of Registrant as Specified in Its Charter)


          Delaware                                              41-1464066
-------------------------------                           ----------------------
(State or Other Jurisdiction of                              (I.R.S. Employer
Incorporation or Organization)                            Identification Number)

  Suite 100, One Post Oak Central                               77056-4400
  2000 Post Oak Boulevard, Houston, TX                          ----------
---------------------------------------                         (Zip Code)
(Address of Principal Executive Offices)


       Registrant's Telephone Number, Including Area Code: (713) 296-6000



Indicate by check mark whether the registrant (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 registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.


                                 YES  X   NO
                                     ---      ---


<PAGE>   2


                         PART I - FINANCIAL INFORMATION


ITEM 1 - FINANCIAL STATEMENTS


                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                               STATEMENT OF INCOME
                                   (UNAUDITED)


<TABLE>
<CAPTION>
                                                     FOR THE QUARTER              FOR THE SIX MONTHS
                                                      ENDED JUNE 30,                ENDED JUNE 30,
                                                -------------------------     -------------------------
                                                   1999           1998           1999           1998
                                                ----------     ----------     ----------     ----------
<S>                                             <C>            <C>            <C>            <C>
REVENUES:
   Oil and gas production revenues              $2,058,107     $2,153,787     $3,721,885     $4,349,472
   Interest income                                  19,456         15,437         35,806         25,248
                                                ----------     ----------     ----------     ----------

                                                 2,077,563      2,169,224      3,757,691      4,374,720
                                                ----------     ----------     ----------     ----------

EXPENSES:
   Depreciation, depletion and amortization        825,499        725,513      1,499,119      1,447,988
   Lease operating expense                         199,123        184,833        352,988        390,489
   Administrative                                  135,000        140,952        270,000        275,952
                                                ----------     ----------     ----------     ----------

                                                 1,159,622      1,051,298      2,122,107      2,114,429
                                                ----------     ----------     ----------     ----------

NET INCOME                                      $  917,941     $1,117,926     $1,635,584     $2,260,291
                                                ==========     ==========     ==========     ==========

NET INCOME ALLOCATED TO:
   Managing Partner                             $  296,275     $  313,053     $  528,036     $  630,598
   Investing Partners                              621,666        804,873      1,107,548      1,629,693
                                                ----------     ----------     ----------     ----------

                                                $  917,941     $1,117,926     $1,635,584     $2,260,291
                                                ==========     ==========     ==========     ==========

NET INCOME PER INVESTING PARTNER UNIT           $      545     $      683     $      971     $    1,379
                                                ==========     ==========     ==========     ==========

WEIGHTED AVERAGE INVESTING PARTNER
   UNITS OUTSTANDING                                 1,141        1,179.3          1,141        1,181.7
                                                ==========     ==========     ==========     ==========
</TABLE>


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

                                        1


<PAGE>   3



                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                             STATEMENT OF CASH FLOWS
                                   (UNAUDITED)


<TABLE>
<CAPTION>
                                                                           FOR THE SIX MONTHS ENDED JUNE 30,
                                                                           ----------------------------------
                                                                               1999                   1998
                                                                           -----------            -----------
<S>                                                                        <C>                    <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
   Net income                                                              $ 1,635,584            $ 2,260,291
   Adjustments to reconcile net income to net cash
      provided by operating activities:
         Depreciation, depletion and amortization                            1,499,119              1,447,988
         Changes in operating assets and liabilities:
             Decrease (increase) in accrued revenues receivable                794,436                (85,718)
             Increase (decrease) in accrued operating expenses payable          22,467               (103,743)
             (Decrease) increase in payable to/receivable from
                 Apache Corporation                                           (220,744)               293,827
                                                                           -----------            -----------
         Net cash provided by operating activities                           3,730,862              3,812,645
                                                                           -----------            -----------
CASH FLOWS FROM INVESTING ACTIVITIES:
   Additions to oil and gas properties                                        (580,421)            (1,830,120)
   Non-cash portion of oil and gas property additions                          (64,545)              (622,547)
   Proceeds from sales of oil and gas properties                               140,620                363,534
   Increase in drilling advances                                                    --                (69,012)
                                                                           -----------            -----------
         Net cash used in investing activities                                (504,346)            (2,158,145)
                                                                           -----------            -----------
CASH FLOWS FROM FINANCING ACTIVITIES:
   Repurchase of Partnership Units                                                  --               (348,000)
   Distributions to Investing Partners                                        (855,728)                    --
   Distributions to Managing Partner, net                                     (921,710)              (501,252)
                                                                           -----------            -----------
         Net cash used in financing activities                              (1,777,438)              (849,252)
                                                                           -----------            -----------

NET INCREASE IN CASH AND CASH EQUIVALENTS                                    1,449,078                805,248

CASH AND CASH EQUIVALENTS, BEGINNING OF YEAR                                 1,324,949                691,797
                                                                           -----------            -----------
CASH AND CASH EQUIVALENTS, END OF PERIOD                                   $ 2,774,027            $ 1,497,045
                                                                           ===========            ===========

</TABLE>


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

                                        2


<PAGE>   4


                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                                  BALANCE SHEET
                                   (UNAUDITED)


<TABLE>
<CAPTION>
                                                                      JUNE 30,         DECEMBER 31,
                                                                       1999               1998
                                                                   -------------      -------------
<S>                                                                <C>                <C>
                                  ASSETS
CURRENT ASSETS:
   Cash and cash equivalents                                       $   2,774,027      $   1,324,949
   Accrued revenues receivable                                           503,563          1,297,999
   Receivable from Apache Corporation                                    150,771                 --
                                                                   -------------      -------------
                                                                       3,428,361          2,622,948
                                                                   -------------      -------------

OIL AND GAS PROPERTIES, on the basis of full cost accounting:
   Proved properties                                                 168,771,501        168,331,700
   Less - Accumulated depreciation, depletion and amortization      (162,613,213)      (161,114,094)
                                                                   -------------      -------------
                                                                       6,158,288          7,217,606
                                                                   -------------      -------------
                                                                   $   9,586,649      $   9,840,554
                                                                   =============      =============

                    LIABILITIES AND PARTNERS' CAPITAL

CURRENT LIABILITIES:
   Accrued exploration and development                             $     527,375      $     591,920
   Accrued operating expenses payable and other                          120,834             98,367
   Payable to Apache Corporation                                              --             69,973
                                                                   -------------      -------------
                                                                         648,209            760,260
                                                                   -------------      -------------

PARTNERS' CAPITAL:
   Managing Partner                                                      203,386            597,060
   Investing Partners (1,141.0 and 1,141.0 units
      outstanding, respectively)                                       8,735,054          8,483,234
                                                                   -------------      -------------
                                                                       8,938,440          9,080,294
                                                                   -------------      -------------
                                                                   $   9,586,649      $   9,840,554
                                                                   =============      =============
</TABLE>


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

                                        3


<PAGE>   5


                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                          NOTES TO FINANCIAL STATEMENTS
                                   (UNAUDITED)


     The financial statements included herein have been prepared by the Apache
Offshore Investment Partnership (the Partnership), without audit, pursuant to
the rules and regulations of the Securities and Exchange Commission, and reflect
all adjustments which are, in the opinion of management, necessary for a fair
statement of the results for the interim periods, on a basis consistent with the
annual audited financial statements. All such adjustments are of a normal,
recurring nature. Certain information, accounting policies, and footnote
disclosures normally included in financial statements prepared in accordance
with generally accepted accounting principles have been omitted pursuant to such
rules and regulations, although the Partnership believes that the disclosures
are adequate to make the information presented not misleading. These financial
statements should be read in conjunction with the financial statements and the
summary of significant accounting policies and notes thereto included in the
Partnership's latest annual report on Form 10-K.


1.   RECEIVABLE FROM/PAYABLE TO APACHE

     Receivable from/payable to Apache Corporation, the Partnership's managing
partner (Apache or the Managing Partner), represents the net result of the
Investing Partners' revenue and expenditure transactions in the current month.
Generally, cash in this amount will be transferred from/to Apache in the month
after the Partnership's transactions are processed and the net results of
operations are determined.


2.   RIGHT OF PRESENTMENT

     As provided in the Partnership Agreement, as amended (the Amended
Partnership Agreement), a first right of presentment offer for 1999 of $8,410
per Unit, plus interest to the date of the payment, was made to Investing
Partners based on a valuation date of December 31, 1998. As a result, the
Partnership agreed in July 1999 to acquire 5.14835 Units for a total of $45,000
in cash. As provided in the Amended Partnership Agreement, Investing Partners
will have a second right of presentment during the fourth quarter of 1999, based
on a valuation date of June 30, 1999.

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



                                       4
<PAGE>   6


ITEM 2 -   MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
           RESULTS OF OPERATIONS


RESULTS OF OPERATIONS

NET INCOME AND REVENUE

     The Partnership reported net income of $.9 million in the second quarter of
1999, versus $1.1 million in the prior year period. Net income per Investing
Partner Unit decreased 20 percent, from $683 per Unit to $545 per Unit. Lower
natural gas production and prices, and higher depreciation, depletion and
amortization (DD&A) expense, contributed to the decline.

     For the first half of 1999, net income of $1.6 million, or $971 per
Investing Partner Unit, decreased 28 percent and 30 percent, respectively, from
$2.3 million, or $1,379 per Investing Partner Unit, in the same period last
year. The declines were attributable to lower natural gas prices and production,
combined with higher DD&A expense.

     Revenues decreased four percent, from $2.2 million in the second quarter of
1998 to $2.1 million in the second quarter of 1999. Natural gas and crude oil
sales represented 74 percent and 25 percent, respectively, of the Partnership's
total revenues during the second quarter of 1999. For the first six months of
1999, oil and gas production revenues decreased 14 percent to $3.7 million as
lower natural gas prices and production more than offset small increases in oil
production and prices. Natural gas and crude oil sales contributed 77 percent
and 22 percent, respectively, to the Partnership's total revenues during the
first half of 1999.

     The Partnership's oil and gas production volume and price information is
summarized in the following table (gas volumes presented in thousand cubic feet
(Mcf) per day):

<TABLE>
<CAPTION>
                                    FOR THE QUARTER ENDED JUNE 30,             FOR THE SIX MONTHS ENDED JUNE 30,
                                ----------------------------------------    ----------------------------------------
                                                             INCREASE                                    INCREASE
                                   1999          1998       (DECREASE)         1999          1998       (DECREASE)
                                ------------  ------------  ------------    ------------  ------------  ------------
<S>                             <C>           <C>           <C>             <C>           <C>           <C>
Gas volume - Mcf per day              8,198         8,943          (8%)           8,717         9,010          (3%)
Average gas price - per Mcf           $2.08         $2.21          (6%)           $1.83         $2.20         (17%)
Oil volume - barrels per day            344           297           16%             330           315            5%
Average oil price - per barrel       $16.30        $13.13           24%          $13.85        $13.33            4%
</TABLE>

SECOND QUARTER 1999 COMPARED TO SECOND QUARTER 1998

     Natural gas production revenues for the second quarter of 1999 totaled $1.5
million, 14 percent lower than the second quarter of 1998. Natural gas prices
decreased six percent for the second quarter of 1999 compared to the
year-earlier period, which negatively impacted revenue by $.1 million. Natural
gas volumes for the quarter declined eight percent from a year ago due, in part,
to downtime for repairs at Ship Shoal 259 and East Cameron 60.

     The Partnership's crude oil production revenues for the second quarter of
1999 totaled $.5 million, a 44 percent increase from the second quarter of 1998.
The $.2 million increase in oil sales was attributable to the 24 percent
increase in average realized oil price and 16 percent increase in oil
production.

YEAR-TO-DATE 1999 COMPARED TO YEAR-TO-DATE 1998

     Gas sales for the first half of 1999 of $2.9 million decreased $.7 million,
or 19 percent, when compared to the same period in 1998. Average realized gas
prices decreased $.37 per Mcf, or 17 percent, when compared with the first six
months of 1998, negatively impacting sales by $.6 million. Gas production for
the first half of 1999 decreased by three percent when compared to the same
period in 1998, negatively impacting revenues by $.1 million. Production
decreases in 1999 were primarily due to natural declines in production.



                                       5
<PAGE>   7

     For the six months ended June 30, 1999, oil sales increased nine percent to
$.8 million when compared to the same period last year. The Partnership's oil
sales revenues were favorably impacted by a five percent increase in oil
production and a four percent increase in realized prices. The increase in oil
production was attributable to recompletion projects.


OPERATING EXPENSES

     The Partnership's DD&A rate, expressed as a percentage of oil and gas
production revenues, was approximately 40 percent during the second quarter and
first six months of 1999, compared to 34 percent and 33 percent, respectively,
during the same periods in 1998. The increases in the DD&A rate was a result of
lower natural gas prices in 1999.

     Lease operating expense (LOE) was eight percent higher in the second
quarter 1999 compared to the second quarter 1998 due to higher repair and
maintenance expense. For the first half of 1999, LOE of $.4 million was down 10
percent from a year ago due to lower workover activity in 1999.


CASH FLOW, LIQUIDITY AND CAPITAL RESOURCES

CAPITAL RESOURCES AND LIQUIDITY

     The Partnership's primary capital resource is net cash provided by
operating activities, which was $3.7 million for the first half of 1999. Net
cash provided by operating activities in 1999 was down two percent from a year
ago, as the 28 percent decrease in net income in 1999 was largely offset by the
impact of reduced revenue receivables. Future cash flows will be influenced
similarly by fluctuations in product prices, production levels and operating
costs.

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.

     During the first six months of 1999, the Partnership's oil and gas property
additions totaled $.6 million. These additions related primarily to
recompletions at South Timbalier Block 295 and drilling activity at North Padre
Block 969. Based on information supplied by the operators of the properties, the
Partnership anticipates capital expenditures of approximately $.9 million for
the remainder of 1999. The anticipated capital expenditures primarily relate to
South Timbalier Block 295. Such estimates may change based on realized prices,
drilling results or changes by the operator to the development plan.

     The Partnership made a distribution to Investing Partners of $750 per Unit
on March 18, 1999. The amount of future distributions will be dependent on
actual and expected production levels, realized and expected oil and gas prices,
expected drilling and recompletion expenditures, and prudent cash reserves for
future dismantlement and abandonment costs that will be incurred after the
Partnership's reserves are depleted.

     As provided in the Amended Partnership Agreement, a first right of
presentment offer for 1999 of $8,410 per Unit, plus interest to the date of
payment, was made to Investing Partners, based on a valuation date of December
31, 1998. As a result, the Partnership agreed in July 1999 to acquire 5.14835
Units for a total of $45,000 in cash. As provided in the Amended Partnership
Agreement, Investing Partners will have a second right of presentment during the
fourth quarter of 1999, based on a valuation date of June 30, 1999. The
Partnership is not in a position to predict how many Units will be presented for
repurchase during the fourth quarter and cannot, at this time, determine if the
Partnership will have sufficient funds available to repurchase Units. The
Partnership has no obligation to purchase any Units presented to the extent it
determines that it has insufficient funds for such purchases. The Amended
Partnership Agreement contains limitations on the number of Units that the
Partnership can repurchase, including a limit of 10 percent of the outstanding
Units on an annual basis.


                                       6
<PAGE>   8
     On May 18, 1999, the Managing Partner acquired from Shell Offshore Inc. and
affiliated Shell entities (Shell) its interest in certain Gulf of Mexico
properties, together with certain production-related assets and proprietary 3D
seismic data. The purchase price, subject to post closing adjustments, was
$686.5 million in cash and one million shares of Apache common stock. The
impact of this acquisition on the Partnership is not known at this time.

     In conjunction with the Shell transaction, Apache acquired Shell's interest
in the South Timbalier 295 field. As an interest-owner in that field, the
Partnership held a preferential right to purchase the acquired interest for $68
million. The Partnership waived that right.


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 June 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                                   August 1999                    90%
</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 has assessed 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. Such responses
indicate they will be compliant by year-end.



                                       7
<PAGE>   9
     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 implementation of the business software project was completed and
operational effective with January 1999 production.

     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 on 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, 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
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. Future oil and gas
prices also could affect results of operations and cash flows.


                                       8
<PAGE>   10


                          PART II - OTHER INFORMATION


ITEM 1.      LEGAL PROCEEDINGS

             None.

ITEM 2.      CHANGES IN SECURITIES

             None.

ITEM 3.      DEFAULTS UPON SENIOR SECURITIES

             None.

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

             None.

ITEM 5.      OTHER INFORMATION

             None.

ITEM 6.      EXHIBITS AND REPORTS ON FORM 8-K

             a.   Exhibits.

                  27.1   Financial Data Schedule.

             b.   Reports on Form 8-K - None.



                                       9
<PAGE>   11


                                   SIGNATURES


Pursuant to the requirements of Section 13 or 15(d) of the Securities Exchange
Act of 1934, the registrant 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



Dated:    August 12, 1999        /s/ Roger B. Plank
                                 -----------------------------------------------
                                 Roger B. Plank
                                 Vice President and Chief Financial Officer


Dated:    August 12, 1999        /s/ Thomas L. Mitchell
                                 -----------------------------------------------
                                 Thomas L. Mitchell
                                 Vice President and Controller
                                 (Chief Accounting Officer)


<PAGE>   12



                                INDEX TO EXHIBITS

<TABLE>
<CAPTION>
Exhibit
Number            Description
-------           -----------
<S>               <C>
27.1       -      Financial Data Table
</TABLE>