<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          SEPTEMBER 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
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(State or other jurisdiction of                      (IRS Employer
incorporation or organization)                     Identification No.)

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

     806-376-1741                                      FAX 806-376-9301
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(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 September 30, 1998, there were 5,414,232 shares of the issuer's common
stock outstanding.

                         This report contains 13 pages.



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<PAGE>   2





                           AMARILLO BIOSCIENCES, INC.


                                      INDEX

<TABLE>
<CAPTION>


PART I:              FINANCIAL INFORMATION                                                                    PAGE NO.
                                                                                                              --------     
<S>                                                                                                                 <C>
Item 1.              Financial Statements (unaudited)

                     Consolidated Balance Sheets - December 31, 1997 and
                     September 30, 1998..........................................................                    3

                     Consolidated Statements of Operations - Three Months and
                     Nine Months Ended September 30, 1997 and 1998 and
                     Cumulative from June 25, 1984 (Inception) through
                     September 30, 1998..........................................................                    4

                     Condensed Consolidated Statements of Cash Flows - Nine
                     Months Ended September 30, 1997 and 1998 and Cumulative
                     from June 25, 1984 (Inception) through September 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,        September 30,
                                                                                             1997                 1998
                                                                                      ------------------   ------------------
<S>                                                                                   <C>                  <C>               
ASSETS
Current assets:
  Cash and cash equivalents                                                           $          879,170   $        5,335,452
  Marketable securities                                                                        6,007,182                   --
  Other current assets                                                                            70,779               51,368
                                                                                      ------------------   ------------------
   Total current assets                                                                        6,957,131            5,386,820
Property and equipment, net                                                                      125,179              120,621
Patent license, net of accumulated amortization of $73,824 and
  $79,323 at December 31, 1997 and September 30, 1998, respectively                               51,176               45,677
Organization cost, net of accumulated amortization of $4,962 and
  $6,084 at December 31, 1997 and September 30, 1998, respectively                                 1,122                   --
Investment in ISI common stock                                                                   114,023                8,203
                                                                                      ------------------   ------------------
Total assets                                                                          $        7,248,631   $        5,561,321
                                                                                      ==================   ==================
LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
  Accounts payable                                                                    $           74,754   $          143,192
  Accrued interest expense                                                                        91,356              179,106
  Other accrued expenses                                                                          47,958               19,061
                                                                                      ------------------   ------------------
    Total current liabilities                                                                    214,068              341,359
Notes payable to related party                                                                 2,600,000            2,600,000
                                                                                      ------------------   ------------------
Total liabilities                                                                              2,814,068            2,941,359
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)         (10,754,196)
  Other comprehensive income (loss)                                                               33,698              (72,122)
                                                                                      ------------------   ------------------
Total stockholders' equity                                                                     4,434,563            2,619,962
                                                                                      ------------------   ------------------
Total liabilities and stockholders' equity                                            $        7,248,631   $        5,561,321
                                                                                      ==================   ==================

</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                Nine months ended              (Inception)
                                          September 30,                      September 30,                 through
                                     ------------------------         -------------------------          September 30,
                                      1997             1998             1997              1998               1998
                                ------------------------------------------------------------------------------------
<S>                             <C>               <C>               <C>               <C>               <C>         
Revenues:
  Contract revenues             $         --      $         --      $         --      $         --      $  9,000,000
  Interferon sales                       402                --               402                --           420,974
  Interest income                    101,821            68,494           323,491           235,969         1,353,787
  Sublicense fees                         --                --                --                --           113,334
  Royalty income                          --                --                --                --            31,544
  Gain on sale of ISI stock               --                --                --                --           188,562
  Other                               26,000                --            52,000                --           604,371
                                ------------------------------------------------------------------------------------
                                     128,223            68,494           375,893           235,969        11,712,572

Expenses:
  Research and
 development expenses                341,015           341,998         1,057,350         1,062,409        11,042,003
  Selling, general, and
 administrative expenses             397,018           235,600           973,007           794,591        10,602,071
  Interest expense                    29,625            29,250            88,875            87,750           787,694
                                ------------------------------------------------------------------------------------
                                     767,658           606,848         2,119,232         1,944,750        22,431,768
                                ------------------------------------------------------------------------------------

Loss before income taxes            (639,435)         (538,354)       (1,743,339)       (1,708,781)      (10,719,196)
Income tax expense                        --                --                --                              35,000
                                ------------------------------------------------------------------------------------
Net loss                        $   (639,435)     $   (538,354)     $ (1,743,339)     $ (1,708,781)     $(10,754,196)
                                ==================================================================================== 
Net loss per share              $      (0.12)     $      (0.10)     $      (0.32)     $      (0.32)
                                ==================================================================   
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>
                                                                      
                                                    Nine months ended               Cumulative from 
                                                      September 30,                   June 25,1984   
                                              -------------------------------     (Inception) through 
                                                   1997              1998            Sept. 30, 1998 
                                              --------------    -------------    ----------------------
<S>                                           <C>               <C>                 <C>          
Net cash used in operating activities         $ (2,019,952)     $ (1,541,335)       $ (9,613,216)
                                              ------------      ------------        ------------ 

Net cash provided by (used in) investing
activities                                           6,870         5,997,617            (528,351)
                                              ------------      ------------        ------------ 
Net cash provided by financing activities               --                --          15,477,019
                                              ------------      ------------        ------------ 
Net increase (decrease) in cash and cash
equivalents                                     (2,013,082)        4,456,282           5,335,452
                                              ------------      ------------        ------------ 
Cash and cash equivalents at beginning of
period                                           2,799,297           879,170                  --
                                              ------------      ------------        ------------ 
Cash and cash equivalents at end of
period                                        $    786,215      $  5,335,452        $  5,335,452
                                              ============      ============        ============ 
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 nine months ended September 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. For comparison purposes with 1998, certain amounts
         have been reclassified from selling, general and administrative
         expenses to research and development expenses for the nine months ended
         September 30, 1997. The impact of the reclassification was $130,308.

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 are 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 September 30, 1998 and 1997, total
         comprehensive loss amounted to ($545,323) and ($639,435). For the nine
         months ended September 30, 1998 and 1997, total comprehensive loss
         amounted to ($1,814,601) and ($1,589,839).

5.       Subsequent Event. On November 5, 1998, the Company confirmed by letter
         its intention to enter into an agreement with Agritek Bio Ingredients
         Corporation ("Agritek"), under which Agritek would expend $250,000 over
         the course of one (1) year for clinical studies in at least two (2)
         animal health indications. Depending upon Agritek's evaluation of the
         results of those studies, Agritek would then make an election to either
         purchase seventy percent (70%) of the voting common stock of the
         Company's animal health subsidiary, Vanguard Biosciences, Inc.
         ("Vanguard"); or, in lieu of acquiring the stock of Vanguard, to
         receive $250,000 worth of the Company's common stock, priced at its
         market value on the date of such election. If Agritek elects to
         purchase seventy percent (70%) of Vanguard, the purchase price will be
         at least $500,000, and no more than $2,000,000, with the actual price
         being contingent upon the speed with which regulatory approval to
         market two animal health products in the US is obtained.


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<PAGE>   7



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

         RESEARCH 

         A confirmatory Phase 2 clinical trial continues in subjects with
         fibromyalgia syndrome (FMS). A market analysis estimated that 7.5
         million Americans suffer from FMS. Our confirmatory Phase 2 trial in
         120 subjects represents a significant step in the Company's strategy to
         develop a 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)
         continues. Our study in subjects who are HIV positive with dry mouth
         (University of Mississippi) was completed; some improvement in oral
         comfort and increased salivation was noted. Nineteen subjects were
         screened and 12 were enrolled; of those, only 5 completed the study but
         the data are useful in a patent application.

         The study in myelofibrotic disease subjects was completed. Ten subjects
         were enrolled with agnogenic myeloid metaplasia and 9 completed the
         course of therapy; 0 of 5 evaluable subjects had a response for
         hemoglobin improvement, 4 with high hemoglobin maintained their
         hemoglobin and 2 of 9 evaluable subjects had at least a partial
         response for both hepatomegaly. One of 6 subjects with primary
         thrombocytopenia had a positive response and 3 of 7 subjects with
         polycythemia vera had at least a partial response. Overall, there were
         some positive responses. However, because other areas of research look
         more promising, and because the principal investigator died of a heart
         attack, the Company does not contemplate further R&D in this area.

         The start of the Phase 3 clinical trial on Sjogren's syndrome was
         delayed while the FDA considered protocol changes. Progress in
         understanding the basic mechanism of action of oral interferon alpha
         continued in the third quarter of 1998. A study of topical interferon
         alpha in dogs and cats continued in the third quarter of 1998. Our
         hepatitis C study in Canada continues.

         A new R&D director, Dr. Phil Fox, agreed to a contract and will join
         the company January 1, 1999. Dr. Fox has a research career spanning 23
         years at the National Institutes of Health, National Institute of
         Dental Research in Bethesda, Maryland, serving most recently as
         clinical director of the Intramural Research Program.



                                        7

<PAGE>   8



         LIQUIDITY AND CAPITAL RESOURCES

         At September 30, 1998, the Company had cash of $5,335,452 with accounts
         payable of $143,192 and other funding commitments for clinical studies
         of approximately $944,449.

         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 12 months.

         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. 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 as of September 30, 1998 otherwise
         proves 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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<PAGE>   9



                           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
September 30, 1998.





 


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<PAGE>   10




                                   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: November 11, 1998                   By: /s/ JOSEPH M. CUMMINS
                                              --------------------------------
                                                   Joseph M. Cummins
                                                   President, Chief Executive 
                                                   Officer and Chief Financial 
                                                   Officer





<PAGE>   11


                                 EXHIBIT INDEX

Exhibit Number                    Description
--------------                  ---------------

     27                     Financial Data Schedule