<PAGE>   1

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                       SECURITIES AND EXCHANGE COMMISSION
                              WASHINGTON, DC 20549

                                  -------------

                                   FORM 10-QSB

                QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
                  FOR THE QUARTERLY PERIOD ENDED MARCH 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: 0-12185

                                  -------------

                          ALASKA APOLLO RESOURCES INC.
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)

          PROVINCE OF BRITISH COLUMBIA                        NOT APPLICABLE
(State or other jurisdiction of incorporation or             (I.R.S. EMPLOYER
                 organization)                             IDENTIFICATION NO.)

         131 PROSPEROUS PLACE, SUITE 17
              LEXINGTON, KENTUCKY                               40509-1844
    (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)                    (ZIP CODE)

       REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE: (606) 263-3948

                                  -------------

         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 .

         THE NUMBER OF SHARES OUTSTANDING OF EACH OF THE REGISTRANT'S CLASSES OF
COMMON STOCK, AS OF MARCH 31, 1998, WAS 9,821,754.

         Transitional Small Business Disclosure Format (check one):  Yes   No X.
                                                                        ---  ---


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<PAGE>   2






                                     PART I
                              FINANCIAL INFORMATION

ITEM 1.  FINANCIAL STATEMENTS.

         The information required by this Item 1 appears on pages 7 through 9 of
this Report, and is incorporated herein by reference.

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

         The following is a discussion of the Company's financial condition and
results of operations. This discussion should be read in conjunction with the
Financial Statements of the Company described in Item 1 of this Report.
Statements contained in this "Management' Discussion and Analysis of Financial
Condition and Results of Operations," which are not historical facts may be
forward looking statements. Such information involves risks and uncertainties,
including those created by general market conditions, competition and the
possibility that events may occur which could limit the ability of the Company
to maintain or improve its operating results or execute its primary growth
strategy. Although management believes that the assumptions underlying the
forward-looking statements are reasonable, any of the assumptions could be
inaccurate, and there can be no assurances that the forward-looking statements
included herein will prove to be accurate. The inclusion of such information
should not be regarded as a representation by management or any other person
that the objectives and plans of the Company will be achieved. Moreover, such
forward-looking statements are subject to certain risks and uncertainties which
could cause actual results to differ materially from those projected. Readers
are cautioned not to place undue reliance on these forward-looking statements 
that speak only as of the date hereof.

         In the fourth quarter of 1993, the Registrant acquired its wholly owned
subsidiary, Daugherty Petroleum, Inc. ("DPI"). Since the acquisition, the
Registrant has been aggressively (1) acquiring natural gas and oil properties in
southeastern and western Kentucky, (2) expanding its natural gas production
through joint ventures and drilling programs for its own account, and (3)
diversifying its revenue and asset base to include other segments of the oil and
gas industry.

         In the fourth quarter of 1996, the Registrant acquired an 80% interest
of Red River Hardwoods, Inc. Since then, the Company has seen increased revenues
from Red River's lumber activities. Management commenced a plan to change Red
River's products mix to products with higher profits, and set about increasing
sales.

         The Company has traditionally realized revenues from its oil and gas
operations and Red River's manufacturing. For the three month quarter ending
March 31, 1998, the Registrant drilled six natural gas wells and completed one
natural gas well. This is in contrast to the same period of 1997 when the
Registrant drilled four natural gas wells and completed one natural gas well.
The drilling performed in the first quarter of 1998 is primarily related to a
joint venture on the Registrant's Farmout acreage from Equitable Resources
Energy Corporation. With the acquisition of Red River Hardwoods, Inc., the
Company has seen increased revenues from Red River's Lumber activities. Lumber
products generated by Red River are furniture dimension parts, architectural
moulding and hardwood flooring.

LIQUIDITY

         The Company continues to acquire natural gas and oil properties.
Daugherty Petroleum, Inc. has provided the Company with a diversified asset base
which includes natural resources other than its original gold and silver mining
properties and has also increased the Company's asset base. During the first
quarter of 1998, management continued to invest in areas it deemed critical in
developing an infrastructure suitable to support its future growth. These areas
included ongoing expenses in management, professional and operational personnel
and other expenses deemed necessary to position the Company for future
acquisitions and financing.


                                       2
<PAGE>   3



         Historically, the Company's revenues have been from its interests in
the producing natural gas and oil wells it operates and owns interest in and
from its activities as "turnkey driller" and operator for various drilling
programs in its geographic area. DPI has reduced its dependence on activities as
"turnkey driller" for private investors and instead concentrated on joint
ventures with industry partners. During the first quarter of 1998, approximately
37% of the Company's revenues were derived from joint venture drilling. Natural
gas and oil operations and revenues accounted for 7% of the revenues. The
Company has begun to see additional revenues from Red River's activities.
Manufacturing sales related to Red River accounted for 56% of the revenues.

         The Company plans to drill 36 wells during 1998 and will attempt to
earn interests ranging from 12.5% to 50% interest in each well it drills.

         Working capital for the period ending March 31, 1998, was a negative
$1,702,968 when compared to the same period in 1997, when working capital was a
negative $529,729.

         During the first quarter of 1998, and compared to the same period in
1997, the changes in the composition of the Company's current assets were: cash
balances increased $430,718 from $179,664 to $610,402; accounts receivable
balances increased $25,019 from $745,048 to $770,067; and inventories decreased
$28 from $587,767 to $587,795. Other current assets such as prepaids and notes
receivable decreased $27,967 from $32,640 to $4,673. Overall, current assets
increased by $427,818 to $1,972,937.

         Current liabilities for the period were $3,675,905 compared to
$2,074,848 for the first quarter of 1997. Drilling pre-payments expected to be
used during 1998 accounted for $1,104,373 of the increase.

         While management believes that the cash flow resulting in its operating
revenues will contribute significantly to its short-term financial commitments
and operating costs, its has developed a plan in 1998 to meet its financial
obligations. The plan includes:

         -    In November 1997, Daugherty Petroleum signed a Letter of Intent to
              acquire producing properties in Kentucky, Louisiana and Tennessee.
              Daugherty Petroleum is continually reviewing existing properties
              in its area of interest that are for sale.
         -    The Company is currently holding negotiations with financial
              institutions with the intent of securing additional financing to
              support existing and future capital requirements for its oil and
              gas operation.
         -    Installation of additional natural gas gathering system. The
              Company plans to expand its natural gas pipeline by 45,000 feet in
              1998. The extension will allow for substantially more natural gas
              to be transported to market from wells drilled in 1997 and 1998.
         -    Additional funding for Red River Hardwoods, Inc. The Company is
              negotiating additional inventory loans for Red River Hardwoods,
              Inc. that will allow it to increase its inventory, thereby
              increasing its revenues.

RESULTS OF OPERATIONS

         For the period ending March 31, 1998, the Company's gross revenues
increased to $1,877,738 from $1,281,087 for the same period in 1998. The Company
experienced a net loss of $64,244 in this period compared to a net loss of
$142,737 in the same period of 1997.

         The Company's gross revenues were derived from drilling contract
revenues of $694,453 (37%); natural gas and oil operations and production
revenues of $138,822 (7%); and lumber sales and product manufacturing revenues
of $1,044,463 (56%).

         The increase in gross revenues of $596,651 was attributable primarily
to the increased drilling activities during the period. Contract revenues from
drilling activities increased by $405,067 from $289,386 in the first quarter of
1997 to $694,453 in the first quarter of 1998. Manufacturing revenues related to
Red River Hardwoods increased by $208,760 from $835,703 in the first quarter of
1997 to $1,044,463 in the first quarter of 1998.



                                       3
<PAGE>   4


         During the first quarter of 1998, total direct costs increased by
$527,202 to $1,592,390 compared to $1,065,188 in the first quarter of 1997.
Direct costs included Red River Hardwoods' expenses and drilling costs of six
natural gas wells.

         The Company believes there are several factors that will increase
revenues for 1998. First, the prices received for natural gas produced are up
over 1997's overall average price. Secondly, the natural gas gathering system
expansion planned for 1998 will dramatically increase Daugherty Petroleum's
ability to transport natural gas to the market. Thirdly, the acquisition of Red
River Hardwoods expands the Company's exploitation of natural resources to
hardwoods in Kentucky.

                                     PART II
                                OTHER INFORMATION

ITEM 1.  LEGAL PROCEEDINGS.

         None.


ITEM 5.  OTHER INFORMATION.

         Not Applicable.

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K.

         (a)      List of Documents Filed with this Report.
                  -----------------------------------------

<TABLE>
<CAPTION>
                                                                                            PAGE
                                                                                            ----
<S>               <C>                                                                       <C>
         (1)      Balance Sheet for the Period Ended March 31, 1998......................     7
                  Income Statement for the Period Ended March 31, 1998...................   8 - 9
</TABLE>

         All schedules have been omitted since the information required to be
submitted has been included in the financial statements or notes or has been
omitted as not applicable or not required.

         (2)      Exhibits--

                  The exhibits indicated by an asterisk (*) are incorporated by
reference.

         EXHIBIT
         NUMBER       DESCRIPTION OF EXHIBIT
         ------       ----------------------

            3(a)*       Memorandum and Articles for Catalina Energy & Resources
                        Ltd., a British Columbia corporation, dated January 31,
                        1979, filed as an exhibit to Form 10 Registration
                        Statement filed May 25, 1984. File No. 0-12185.

            3(b)*       Certificate for Catalina Energy & Resources Ltd., a
                        British Columbia corporation, dated November 27, 1981,
                        changing the name of Catalina Energy & Resources Ltd. to
                        Alaska Apollo Gold Mines Ltd., and further changing the
                        authorized capital of the Company from 5,000,000 shares
                        of common stock, without par value per share, to
                        20,000,000 shares of common stock, without par value per
                        share, filed as an exhibit to Form 10 Registration
                        Statement filed May 25, 1984. File No. 0-12185.

            3(c)*       Certificate of Change of Name for Alaska Apollo Gold
                        Mines Ltd., a British Columbia corporation, dated
                        October 14, 1992, changing the name of Alaska Apollo
                        Gold Mines Ltd. to Alaska Apollo Resources Inc., and
                        further changing the authorized capital of the 



                                       4
<PAGE>   5


                        Company from 20,000,000 shares of common stock, without
                        par value per share, to 6,000,000 shares of common
                        stock, without par value per share.

         3(d)*          Altered Memorandum of Alaska Apollo Resources Inc., a
                        British Columbia corporation, dated September 9, 1994,
                        changing the authorized capital of the Company from
                        6,000,000 shares of common stock, without par value per
                        share, to 20,000,000 shares of common stock, without par
                        value per share.

         4*             See Exhibit No. 3(a).

         10(a)*         Alaska Apollo Resources Inc. 1997 Stock Option Plan,
                        filed as Exhibit 10(a) to Form 10-K for the Company for
                        the fiscal year ended December 31, 1996. (File No.
                        0-12185).

         10(b)*         Incentive Stock Option Agreement by and between Alaska
                        Apollo Resources Inc. and William S. Daugherty dated
                        March 7, 1997, filed as Exhibit 10(b) to Form 10-K for
                        the Company for the fiscal year ended December 31, 1996.
                        (File No. 0-12185).

         10(c)*         Warrant Agreement by and between Alaska Apollo Resources
                        Inc. and Jayhead Investments Limited dated March 7,
                        1997, filed as Exhibit 10(c) to Form 10-K for the
                        Company for the fiscal year ended December 31, 1996.
                        (File No. 0-12185).

         10(d)*         Warrant Agreement by and between Alaska Apollo Resources
                        Inc. and Trio Growth Trust dated March 7, 1997, filed as
                        Exhibit 10(d) to Form 10-K for the Company for the
                        fiscal year ended December 31, 1996. (File No. 0-12185).

         10(e)*         Warrant Agreement by and between Alaska Apollo Resources
                        Inc. and Exergon Capital S.A. dated March 7, 1997, filed
                        as Exhibit 10(e) to Form 10-K for the Company.

         11             Computation of Per Share Earnings

         27             Financial Data Schedule.

         (b)      Reports on Form 8-K.
                  --------------------

                  None

         (c)      Financial Statement Schedules.
                  ------------------------------

                  No schedules are required as all information required has been
                  presented in the audited financial statements.

                                   SIGNATURES

         Pursuant to the requirements of the Securities Exchange Act of 1934,
the Registrant has duly caused this report to be signed on its behalf of the
undersigned hereunto duly authorized.

                                         ALASKA APOLLO RESOURCES INC.


                                         By:  /s/ William S. Daugherty
                                              --------------------------------
                                               William S. Daugherty, President


Dated:   May 15, 1998




                                       5
<PAGE>   6


         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
Registrant and in the capacities and on the dates indicated.

<TABLE>
<CAPTION>
       Signature                                            Title                                  Date     
       ---------                                            -----                                  ----   

<S>                                               <C>                                          <C>
/s/ William S. Daugherty                          Chairman of the Board, President             May 15, 1998
-------------------------                              Director of the Registrant                 
WILLIAM S. DAUGHERTY


James K. Klyman*                                       Director of the Registrant              May 15, 1998
-------------------------
JAMES K. KLYMAN


Charles L. Cotterell*                                  Director of the Registrant              May 15, 1998
-------------------------
CHARLES L. COTTERELL


/s/ Daryl J. Greattinger                               Chief Financial Officer                May 15, 1998
--------------------------
DARYL J. GREATTINGER

*By William S. Daugherty
-----------------------------------
    William S. Daugherty,
    Attorney-in-Fact
</TABLE>

                                       6
<PAGE>   7
ALASKA APOLLO RESOURCES, INC.
SUMMARY CONSOLIDATED BALANCE SHEETS
(United States Dollars)
Unaudited

<TABLE>
<CAPTION>

                                                     3/31/97           3/31/98
                                                  ------------     ------------
                        ASSETS
                        ------
CURRENT ASSETS
--------------
<S>                                               <C>              <C>         
  Cash                                            $    179,664     $    610,402
  Accounts receivable                                  745,048          770,067
  Inventory                                            587,767          587,795
  Other current assets                                  32,640            4,673
                                                  ------------     ------------
              TOTAL CURRENT ASSETS                   1,545,119        1,972,937

OIL & GAS PROPERTIES (NET)                           4,311,522        4,298,261

MINING PROPERTY (NET)                               11,231,247       11,227,733

PROPERTY  & EQUIPMENT (NET)                          2,099,732        1,900,943

OTHER ASSETS
  Related party loans                                   55,557           86,023
  Bonds & deposits                                      57,643           41,000
  Other assets                                         270,488          315,569
  Goodwill, net of amortization of $847,843          1,467,293        1,256,826
                                                  ------------     ------------
                                                     1,850,981        1,699,418
                                                  ------------     ------------
              TOTAL ASSETS                        $ 21,038,601     $ 21,099,292
                                                  ============     ============

            LIABILITIES & STOCKHOLDER'S EQUITY
            ----------------------------------
CURRENT LIABILITIES
  Short-term loans & notes                        $     52,000     $     32,000
  Current portion of LT debt                           527,561          619,203
  Accounts payable                                     967,021        1,205,534
  Accrued liabilities                                  528,266          714,795
  Drilling prepayments                                    --          1,104,373
                                                  ------------     ------------

              TOTAL CURRENT LIABILITIES              2,074,848        3,675,905

LONG-TERM LIABILITIES                                3,627,469        3,390,988

PAYABLE TO RELATED PARTIES                                --             43,529
                                                  ------------     ------------
                                                     5,702,317        7,110,422

MINORITY INTEREST                                        8,638           12,264

STOCKHOLDER'S EQUITY
  Common stock                                      20,395,470       20,954,436
  Common stock subscribed                              125,000           23,055
  Additional paid in capital                              --               --
  Retained earnings (deficit)                       (5,050,087)      (6,936,641)
  Current income (loss)                               (142,737)         (64,244)
                                                  ------------     ------------
                                                    15,327,646       13,976,606
                                                  ------------     ------------

              TOTAL LIABILITIES &
                STOCKHOLDER'S EQUITY              $ 21,038,601     $ 21,099,292
                                                  ============     ============
</TABLE>


Unaudited-Internally prepared by Company management

                                      7

<PAGE>   8

<TABLE>
<CAPTION>
ALASKA APOLLO RESOURCES, INC.
SUMMARY CONSOLIDATED STATEMENTS OF INCOME
(United States Dollars)
Unaudited
                                                      For the three month period ended
                                                                   3/31/97                                3/31/98
                                                       -----------------------------      -----------------------------
<S>                                                    <C>                    <C>         <C>                    <C>    
GROSS REVENUE                                          $ 1,281,087            100.00%     $   1,877,738          100.00%
                                                                                                                       

DIRECT EXPENSES                                          1,065,188             83.15%         1,592,390           84.80%
                                                       -----------     -------------      -------------   -------------

              GROSS PROFIT                                 215,899             16.85%           285,348           15.20%

GENERAL & ADMINISTRATIVE EXPENSES
  Salaries & wages                                          82,716              6.46%            71,123            3.79%
  Accounting & audit                                        21,155              1.65%            50,411            2.68%
  Advertising & promotion                                   13,789              1.08%             2,452            0.13%
  Amortization                                              52,617              4.11%            52,617            2.80%
  Bad debts                                                  2,793              0.22%              --              0.00%
  Depreciation                                              16,726              1.31%            16,820            0.90%
  General consulting                                        17,597              1.37%            16,667            0.89%
  Insurance                                                 20,910              1.63%            13,615            0.73%
  Legal                                                     28,355              2.21%            14,429            0.77%
  Office & general                                          19,923              1.56%            53,267            2.84%
  Payroll & property tax                                     7,571              0.59%             3,871            0.21%
  Rent                                                      13,550              1.06%             8,215            0.44%
  Repairs & maintenance                                      2,865              0.22%             1,791            0.10%
  Shareholder & investor information                           549              0.04%             4,290            0.23%
  Travel & entertainment                                    11,524              0.90%            13,183            0.70%
                                                       -----------     -------------      -------------   -------------

              TOTAL G & A EXPENSES                         312,640             24.40%           322,751           17.19%

OTHER INCOME (EXPENSE)
  Interest & dividend income                                 1,383              0.11%            10,519            0.56%
  Miscellaneous                                              7,025              0.55%            19,902            1.06%
  Gain (loss) on sale of equipment                          13,845              1.08%              --              0.00%
  Interest expense                                         (60,368)            -4.71%           (45,755)          -2.44%
                                                       -----------     -------------      -------------   -------------

INCOME BEFORE INCOME TAX & OTHER                          (134,856)           -10.53%           (52,737)          -2.81%
                                                                                                          

  Income tax expense (benefit)                                --                0.00%              --              0.00%

MINORITY PORTION                                            (7,881)            -0.62%           (11,507)          -0.61%
                                                       -----------     -------------      -------------   -------------

              NET INCOME (LOSS)                        $  (142,737)           -11.14%     $     (64,244)          -3.42%
                                                       ===========     =============      =============   =============


DEFICIT, beginning of period                            (5,050,087)                        $ (6,936,641)
DEFICIT, end of period                                  (5,192,824)                        $ (7,000,885)


Shares outstanding                                       8,504,954                            9,821,754

EARNINGS PER SHARE                                      ($    0.02)                           ($   0.01)

</TABLE>


Unaudited-Internally prepared by Company management


                                      8

<PAGE>   9
<TABLE>
<CAPTION>
SUMMARY CONSOLIDATED STATEMENTS OF CASH FLOWS
(United States Dollars)
Unaudited
                                                                     For the three month period ended

                                                                      3/31/97          3/31/98
                                                                     ---------     ----------- 

<S>                                                                  <C>           <C>         
CASH FLOWS FROM OPERATING ACTIVITIES
  Net income (loss)                                                  $(142,737)    $   (64,244)
  Adjustments to reconcile net income (loss) to net cash
  cash provided by operating activities:
    Depreciation, depletion, & amortization                            129,841         139,976
    Minority interest                                                    7,881          11,507
    Changes in current assets & liabilities
      (Increase) decrease in:
        Accounts receivable                                            (52,720)       (276,345)
        Inventory                                                       (7,452)         90,349
        Other current assets                                             1,070          59,989
      Increase (decrease) in:
        Short-term loans & notes                                          --           (34,100)
        Accounts payable                                                29,611        (267,178)
        Accrued liabilities                                               --           354,399
        Drilling prepayments                                              --          (298,934)
                                                                     ---------     -----------
              Net cash provided by (used in) operating activities      (34,506)       (284,581)


CASH FLOWS FROM INVESTING ACTIVITIES
  Change in oil & gas properties                                       (73,721)       (360,266)
  Change in mining properties                                             --             4,496
  Change in property & equipment                                          --           (22,372)
  Change in other assets                                              (122,950)       (101,607)
                                                                     ---------     -----------
              Net cash provided by (used in) investing activities     (196,671)       (479,749)


CASH FLOWS FROM FINANCING ACTIVITIES
  Issuance of common stock                                                --            23,055
  Change in long-term liabilities                                      139,751          94,911
  Change in payable to related party                                      --            17,206
                                                                     ---------     -----------
              Net cash provided by (used in) financing activities      139,751         135,172
                                                                     ---------     -----------

NET INCREASE (DECREASE) IN CASH                                        (91,426)       (629,158)
                                                                                   -----------

CASH AT BEGINNING OF PERIOD                                            271,090       1,239,560
                                                                     ---------     -----------

CASH AT END OF PERIOD                                                $ 179,664     $   610,402
                                                                     =========     ===========
</TABLE>





Unaudited-Internally prepared by Company management




                                      9