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


                                   FORM 10-QSB


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


For the quarterly period ended                       JUNE 30, 1998
                               -----------------------------------


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

                         Commission File Number 0-20791


                           AMARILLO BIOSCIENCES, INC.
--------------------------------------------------------------------------------
        (Exact name of small business issuer as specified in its charter)

         TEXAS                                            75-1974352
--------------------------------------------------------------------------------
(State or other jurisdiction of                          (IRS Employer
incorporation or organization)                         Identification No.)

800 West Ninth, Amarillo, TX                                  79101
--------------------------------------------------------------------------------
(Address of principal executive offices)                    (Zip Code)

     806-376-1741                                       FAX 806-376-9301
--------------------------------------------------------------------------------
(Issuer's telephone number, including area code)


         Check whether the issuer (1) filed all reports required to be filed by
Section 13 or 15(d) of the Exchange Act during the past 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  .
                                                                      ---    --

As of June 30, 1998, there were 5,414,232 shares of the issuer's common stock
outstanding.

                         This report contains 13 pages.


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                           AMARILLO BIOSCIENCES, INC.


                                      INDEX



<TABLE>
<CAPTION>
PART I:              FINANCIAL INFORMATION                                                                    PAGE NO.
                                                                                                              --------
<S>                  <C>                                                                                      <C>
Item 1.              Financial Statements (unaudited)
                     Consolidated Balance Sheets - December 31, 1997 and
                     June 30, 1998...............................................................                    3
                     Consolidated Statements of Operations - Three Months and
                     Six Months Ended June 30, 1997 and 1998 and Cumulative
                     from June 25, 1984 (Inception) through June 30, 1998........................                    4
                     Condensed Consolidated Statements of Cash Flows - Six
                     Months Ended June 30, 1997 and 1998 and Cumulative
                     from June 25, 1984 (Inception) through June 30, 1998........................                    5
                     Notes to Consolidated Financial Statements..................................                    6

Item 2.              Update to Management's 1998 Plan of Operation...............................                    7
                     Liquidity and Capital Resources.............................................                    8

PART II:             OTHER INFORMATION

Item 6.              Exhibits and Reports on Form 8-K............................................                    9
Signatures           ............................................................................                   10
</TABLE>





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<PAGE>   3




                   AMARILLO BIOSCIENCES, INC. AND SUBSIDIARIES
                      (COMPANIES IN THE DEVELOPMENT STAGE)
                           CONSOLIDATED BALANCE SHEETS
                                   (unaudited)

<TABLE>
<CAPTION>

                                                                                    December 31,              June 30,
                                                                                        1997                    1998
                                                                                  -----------------       -----------------
ASSETS
<S>                                                                               <C>                     <C>              
Current assets:
  Cash and cash equivalents                                                       $         879,170       $         438,315
  Marketable securities                                                                   6,007,182               5,441,261
  Other current assets                                                                       70,779                  18,794
                                                                                  -----------------       -----------------
   Total current assets                                                                   6,957,131               5,898,370
Property and equipment, net                                                                 125,179                 125,685
Patent license, net of accumulated amortization of $73,824 and
  $77,470 at December 31, 1997 and June 30, 1998, respectively                               51,176                  47,530
Organization cost, net of accumulated amortization of $4,962 and
  $6,084 at December 31, 1997 and June 30, 1998, respectively                                 1,122                      --
Investment in ISI common stock                                                              114,023                  15,172
                                                                                  -----------------       -----------------
Total assets                                                                      $       7,248,631       $       6,086,757
                                                                                  =================       =================
LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
  Accounts payable                                                                $          74,754       $         152,815
  Accrued interest expense                                                                   91,356                 149,856
  Other accrued expenses                                                                     47,958                  18,801
                                                                                  -----------------       -----------------
    Total current liabilities                                                               214,068                 321,472
Notes payable to related party                                                            2,600,000               2,600,000
                                                                                  -----------------       -----------------
Total liabilities                                                                         2,814,068               2,921,472

STOCKHOLDERS' EQUITY:
  Common stock, $.01 par value:
    Authorized shares - 10,000,000
    Issued shares - 5,414,232                                                                54,142                  54,142
  Additional paid-in capital                                                             13,392,138              13,392,138
  Deficit accumulated during the development stage                                       (9,045,415)            (10,215,842)
  Other comprehensive income (loss)                                                          33,698                 (65,153)
                                                                                  -----------------       -----------------
Total stockholders' equity                                                                4,434,563               3,165,285
                                                                                  -----------------       -----------------
Total liabilities and stockholders' equity                                        $       7,248,631       $       6,086,757
                                                                                  =================       =================
</TABLE>

                             See accompanying notes.


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<PAGE>   4





                   AMARILLO BIOSCIENCES, INC. AND SUBSIDIARIES
                      (COMPANIES IN THE DEVELOPMENT STAGE)

                      CONSOLIDATED STATEMENTS OF OPERATIONS
                                   (unaudited)

<TABLE>
<CAPTION>

                                                                                                                    Cumulative
                                                                                                                       from
                                                                                                                     June 25,
                                                                                                                       1984
                                          Three months ended                       Six months ended                 (Inception)
                                               June 30,                                June 30,                       through 
                                         --------------------                     ------------------                  June 30,
                                           1997               1998              1997                 1998               1998
                                 -------------------------------------  --------------------------------------  ------------------
<S>                              <C>                 <C>                <C>                 <C>                 <C>               
Revenues:
  Contract revenues              $              -    $             -    $              -    $              -    $        9,000,000
  Interferon sales                               --                 --                  --                  --             420,974
  Interest income                           120,602             77,664             221,670             167,475           1,285,293
  Sublicense fees                                --                 --                  --                  --             113,334
  Royalty income                                 --                 --                  --                  --              31,544
  Gain on sale of ISI stock                      --                 --                  --                  --             188,562
  Other                                          --                 --              26,000                  --             604,371
                                 ------------------  -----------------  ------------------  ------------------  ------------------
                                 $          120,602  $          77,664  $          247,670  $          167,475  $       11,644,078

Expenses:
  Research and
    development expenses                    327,702            351,894             705,438             720,411          10,700,005
  Selling, general, and
    administrative expenses                 323,154            260,312             586,886             558,991          10,366,471
  Interest expense                           29,625             29,250              59,250              58,500             758,444
                                 ------------------  -----------------  ------------------  ------------------  ------------------
                                 $          680,481  $         641,456  $        1,351,574  $        1,337,902  $       21,824,920
                                 ------------------  -----------------  ------------------  ------------------  ------------------

Loss before income taxes                  (559,879)          (563,792)         (1,103,904)         (1,170,427)        (10,180,842)
Income tax expense                               --                 --                  --                  --              35,000
                                 ------------------  -----------------  ------------------  ------------------  ------------------
Net loss                         $        (559,879)  $       (563,792)  $      (1,103,904)  $      (1,170,427)  $     (10,145,842)
                                 ==================  =================  ==================  ==================  ==================
Net loss per share               $           (0.10)  $          (0.10)  $           (0.20)  $           (0.22)
                                 ==================  =================  ==================  ==================
Weighted average shares      
  outstanding                            5,414,232          5,414,232           5,414,232           5,414,232
                                 ==================  =================  ==================  ==================
</TABLE>




                             See accompanying notes.

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<PAGE>   5






                   AMARILLO BIOSCIENCES, INC. AND SUBSIDIARIES
                      (COMPANIES IN THE DEVELOPMENT STAGE)

                 CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
                                   (unaudited)

<TABLE>
<CAPTION>

                                                                          Six months ended                    Cumulative from
                                                                               June 30,                         June 25,1984
                                                            --------------------------------------------    (Inception) through
                                                                    1997                    1998                June 30, 1998 
                                                            ------------------      ------------------      ------------------

<S>                                                         <C>                     <C>                     <C>
Net cash used in operating activities                       $       (1,263,323)     $         (997,211)     $       (9,069,092)
                                                            ------------------      ------------------      ------------------
Net cash provided by (used in) investing
activities                                                              (2,945)                556,356              (5,969,612)
                                                            ------------------      ------------------      ------------------
Net cash provided by financing
activities                                                                  --                      --              15,477,019
                                                            ------------------      ------------------      ------------------
Net decrease in cash and cash
equivalents                                                         (1,266,268)               (440,855)                438,315
                                                            ------------------      ------------------      ------------------
Cash and cash equivalents at beginning
of period                                                            2,799,297                 879,170                      --
                                                            ------------------      ------------------      ------------------
Cash and cash equivalents at end of
period                                                      $        1,533,029      $          438,315      $          438,315
                                                            ==================      ==================      ==================
Supplemental Disclosure of Cash Flow
Information
Cash paid for income taxes                                  $               --      $               --      $           37,084
                                                            ==================      ==================      ==================
                                                            $               --      $               --      $            6,466
Cash paid for interest
</TABLE>


                             See accompanying notes.


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<PAGE>   6





                   AMARILLO BIOSCIENCES, INC. AND SUBSIDIARIES
                      (COMPANIES IN THE DEVELOPMENT STAGE)

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

1.       Basis of Presentation.  The accompanying consolidated financial
         statements, which should be read in conjunction with the consolidated
         financial statements and footnotes included in the Company's Form
         10-KSB for the year ended December 31, 1997, are unaudited (except for
         the December 31, 1997 consolidated balance sheet which was derived from
         the Company's audited financial statements), but have been prepared in
         accordance with generally accepted accounting principles for interim
         financial information. Accordingly, they do not include all of the
         information and footnotes required by generally accepted accounting
         principles for complete financial statements. In the opinion of
         management, all adjustments (consisting only of normal recurring
         adjustments) considered necessary for a fair presentation have been
         included.

         Operating results for the six months ended June 30, 1998 are not
         necessarily indicative of the results that may be expected for the full
         year ending December 31, 1998.

2.       Loss per share. Loss per share is computed based on the weighted
         average number of common shares outstanding.

3.       Reclassification. Certain amounts have been reclassified from selling,
         general and administrative expenses to research and development
         expenses for the six months ended June 30, 1997. The impact of the
         reclassification was $119,411.

4.       Comprehensive income.  As of January 1, 1998, the Company adopted
         Financial Accounting Standards Board Statement No. 130 (Statement 130),
         Reporting Comprehensive Income. Statement 130 establishes new rules for
         the reporting and display of comprehensive income and its components;
         however, the adoption of this Statement has no impact on the Company's
         results of operations or shareholders' equity. Statement 130 requires
         unrealized gains or losses on the Company's available-for-sale
         securities, which prior to adoption were reported separately in
         shareholders' equity, to be included in other comprehensive income.
         Prior year financial statements have been reclassified to conform to
         the requirements of Statement 130.

         For the three months ended June 30, 1998 and 1997, total comprehensive
         loss amounted to ($642,136) and ($398,379). For the six months ended
         June 30, 1998 and 1997, total comprehensive loss amounted to
         ($1,269,273) and ($950,404).



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ITEM 2.           UPDATE TO MANAGEMENT'S 1998 PLAN OF OPERATION

                  RESEARCH

                  A confirmatory Phase 2 clinical trial was started in subjects
                  with fibromyalgia syndrome (FMS). A market analysis estimated
                  that 7.5 million Americans suffer from FMS. Our confirmatory
                  Phase 2 trial in 180 subjects represents a significant step in
                  the Company's strategy to develop an FDA approved treatment.
                  As of now, there are no products approved in the US for FMS;
                  currently patients are treated with pain relieving drugs and
                  antidepressants which are approved for other indications. Our
                  clinical trials in human immunodeficiency virus (HIV) positive
                  subjects with oral warts (University of California San
                  Francisco) and HIV positive with dry mouth (University of
                  Mississippi) and our study in myelofibrotic disease subjects
                  are continuing and moving toward completion, probably in the
                  third quarter of 1998. The start of the Phase 3 clinical trial
                  on Sjogren's syndrome was delayed while the FDA reviewed our
                  Phase 2 data. Suggestions from the FDA will guide us as we
                  seek to initiate the Sjogren's syndrome study in the third
                  quarter of 1998. Progress in understanding the basic mechanism
                  of action of oral interferon alpha continued in the second
                  quarter of 1998. A study of topical interferon alpha in dogs
                  and cats continued in the second quarter of 1998.




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<PAGE>   8




                  LIQUIDITY AND CAPITAL RESOURCES

                  At June 30, 1998, the Company had cash of $438,315 and
                  marketable securities of $5,441,261 with accounts payable of
                  $152,815 and other funding commitments for clinical studies of
                  approximately $659,000.

                  The Company intends to continue to focus its development
                  activities on the treatment of Sjogren's syndrome,
                  fibromyalgia, opportunistic infections in patients who are HIV
                  positive and hepatitis C, and in addition, is considering the
                  commencement of research into myeloproliferative diseases and
                  hepatitis B.

                  The Company anticipates, based on its currently proposed plans
                  and assumptions relating to its operations (including
                  assumptions regarding the progress of its research and
                  development and the timing and costs associated with its
                  development projects), that the Company's existing capital
                  resources will be sufficient to satisfy the Company's
                  estimated cash requirements for at least the next 18-21
                  months. Unless the Company generates significant revenues
                  during such period, the Company will need additional financing
                  to fully fund such development. Moreover, the Company's
                  estimate of the amount required to complete its development
                  projects may prove to be inaccurate. The Company has no
                  current arrangements with respect to, or sources of,
                  additional financing and it is not anticipated that any of the
                  officers, directors or shareholders of the Company will
                  provide any portion of the Company's future financing
                  requirements. There can be no assurance that, when needed,
                  additional financing will be available to the Company on
                  commercially reasonable terms, or at all. In the event that
                  the Company's plans change, its assumptions change or prove
                  inaccurate, or if the Company's existing cash and marketable
                  securities as of June 30, 1998 otherwise prove to be
                  insufficient to fund operations, the Company could be required
                  to seek additional financing sooner than currently
                  anticipated. Any inability to obtain additional financing when
                  needed would have a material adverse effect on the Company,
                  including requiring the Company to significantly curtail or
                  possibly cease its operations.



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                           PART II - OTHER INFORMATION

ITEM 6.           EXHIBITS AND REPORTS ON FORM 8-K

                  Exhibit 27.   Financial Data Schedule



                  No reports on Form 8-K were filed during the quarter ended
June 30, 1998.




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                                   SIGNATURES





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



                                        AMARILLO BIOSCIENCES, INC.


Date: August 13, 1998                 By:/s/ JOSEPH M. CUMMINS
                                         ----------------------------------
                                           Joseph M. Cummins
                                           President, Chief Executive Officer
                                           and Chief Financial Officer







<PAGE>   11
                               INDEX TO EXHIBITS

EXHIBIT
NUMBER                             EXHIBIT
-------                            -------

  27                       Financial Data Schedule