<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             MARCH 31, 1999
                               ------------------------------------------------


[ ]     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 March 31, 1999 there were 5,414,232 shares of the issuer's common stock
outstanding.

                         This report contains 12 pages.



                                        1
<PAGE>   2

                           AMARILLO BIOSCIENCES, INC.


                                      INDEX


<TABLE>
<CAPTION>
PART I:      FINANCIAL INFORMATION                                              PAGE NO.
                                                                                --------
<S>          <C>                                                                <C>
Item 1.      Financial Statements

             Consolidated Balance Sheets - December 31, 1998 and March
             31, 1999...........................................................    3

             Consolidated Statements of Operations - Three Months                    
             Ended March 31, 1998 and 1999 and Cumulative from June                  
             25, 1984 (Inception) through March 31, 1999........................    4

             Condensed Consolidated Statements of Cash Flows - Three                
             Months Ended March 31, 1998 and 1999 and Cumulative                    
             from June 25, 1984 (Inception) through March 31, 1999..............    5

             Notes to Consolidated Financial Statements.........................    6

Item 2.      Management's Discussion and Analysis of Results of                 
             Operations and Financial Condition.................................    7

PART II:     OTHER INFORMATION

Item 6.      Exhibits and Reports on Form 8-K...................................    8

Signatures   ...................................................................    9
</TABLE>




                                        2

<PAGE>   3


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

<TABLE>
<CAPTION>
                                                                    December 31,        March 31,
                                                                        1998              1999
                                                                    ------------      ------------
<S>                                                                 <C>               <C>         
ASSETS
Current assets:
  Cash and cash equivalents                                         $  4,776,328      $  3,855,571
  Other current assets                                                    43,415            46,268
                                                                    ------------      ------------
Total current assets                                                   4,819,743         3,901,839
Property and equipment, net                                              116,761           118,691
Patent license, net of accumulated amortization of $81,177 and
  $82,990 at December 31, 1998 and March 31, 1999, respectively           43,823            42,010
Investment in ISI common stock                                             5,735             5,735
                                                                    ------------      ------------
Total assets                                                        $  4,986,062      $  4,068,275
                                                                    ============      ============
LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
  Accounts payable                                                  $     88,920      $  1,128,546
  Accrued interest                                                       208,356           237,205
  Other accrued liabilities                                               20,722            19,995
                                                                    ------------      ------------
Total current liabilities                                                317,998         1,385,746
Notes payable to related party                                         2,600,000         2,600,000
                                                                    ------------      ------------
Total liabilities                                                      2,917,998         3,985,746
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                   (11,378,216)      (13,363,751)
                                                                    ------------      ------------
Total stockholders' equity                                             2,068,064            82,529
                                                                    ------------      ------------
Total liabilities and stockholders' equity                          $  4,986,062      $  4,068,275
                                                                    ============      ============
</TABLE>

                             See accompanying notes.



                                        3

<PAGE>   4


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

                      CONSOLIDATED STATEMENTS OF OPERATIONS


<TABLE>
<CAPTION>

                                              Three months ended
                                                   March 31,               Cumulative from
                                        ------------------------------      June 25, 1984
                                                                         (Inception) through
                                            1998             1999           March 31, 1999
                                        ------------      ------------   -------------------
<S>                                     <C>               <C>               <C>         
Revenues:
  Contract revenues                     $         --      $         --      $  9,000,000
  Interferon sales                                --                --           420,974
  Interest income                             89,811            48,687         1,463,324
  Sublicense fees                                 --                --           113,334
  Royalty income                                  --                --            31,544
  Gain on ISI stock                               --                --           113,972
  Other                                           --                --           604,431
                                        ------------      ------------      ------------
                                              89,811            48,687        11,747,579

Expenses:
  Research and development
    expenses                                 368,517         1,681,044        13,033,488
  Selling, general, and
    administrative expenses                  298,679           324,329        11,197,049
  Interest expense                            29,250            28,849           845,793
                                        ------------      ------------      ------------
                                             696,446         2,034,222        25,076,330
                                        ------------      ------------      ------------

Loss before income taxes                    (606,635)       (1,985,535)      (13,328,751)
Income tax expense                                --                --            35,000
                                        ------------      ------------      ------------
Net loss                                $   (606,635)     $ (1,985,535)     $(13,363,751)
                                        ============      ============      ============
Basic and diluted loss per share        $      (0.11)     $      (0.37)
                                        ============      ============
Weighted average shares outstanding        5,414,232         5,414,232
                                        ============      ============
</TABLE>


                             See accompanying notes.


                                        4
<PAGE>   5

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

                 CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS


<TABLE>
<CAPTION>
                                                   Three months ended              Cumulative
                                                        March 31,                   from June
                                                                                     25,1984
                                              ------------------------------      (Inception)
                                                                                     through
                                                                                   March 31,
                                                  1998              1999              1999 
                                              ------------      ------------      ------------
<S>                                           <C>               <C>               <C>          
Net cash used in operating activities         $   (575,470)     $   (914,627)     $(11,085,464)
                                              ------------      ------------      ------------
Net cash used in investing activities               (4,441)           (6,130)         (535,984)
                                              ------------      ------------      ------------
Net cash provided by financing activities               --                --        15,477,019
Net increase (decrease) in cash and cash
 equivalents                                      (579,911)         (920,757)        3,855,571
                                              ------------      ------------      ------------
Cash and cash equivalents at beginning
 of period                                         879,170         4,776,328                --
                                              ------------      ------------      ------------
Cash and cash equivalents at end of
 period                                       $    299,259      $  3,855,571      $  3,855,571
                                              ============      ============      ============
Supplemental Disclosure of Cash Flow
  Information
Cash paid for income taxes                    $         --      $         --      $     37,084
                                              ============      ============      ============
Cash paid for interest                        $         --      $         --      $      6,466
                                              ============      ============      ============
</TABLE>

                             See accompanying notes.



                                        5

<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, are unaudited (except for the December 31, 1998 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 three months ended March 31, 1999 are not
         necessarily indicative of the results that may be expected for the full
         year ending December 31, 1999.

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



                                        6

<PAGE>   7



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

                  RESULTS OF OPERATIONS

                  Three Months Ended March 31, 1998 Compared to Three Months
                  Ended March 31, 1999.

                  In the first quarter of 1999 research and development expenses
                  increased significantly to $1,681,044 compared to $368,517 for
                  the first quarter of 1998. This increase was due primarily to
                  the Phase 3 trial in progress for Sjogren's syndrome. Other
                  research and development expenses were incurred for a Phase 2
                  clinical trial for fibromyalgia syndrome.

                  Salary expense totalled $206,938 for the quarter ending March
                  31, 1999 including $159,000 allocated to research and
                  development. For the first quarter of 1998 salary expense was
                  $93,522 including $87,000 allocated to research and
                  development. This increase was due to filling three new
                  positions in the Company. These were a chief operating
                  officer/vice president of business development, director of
                  marketing and director of research and development.

                  LIQUIDITY AND CAPITAL RESOURCES

                  At March 31, 1999 the Company had cash balances of $3,855,571
                  with accounts payable of $1,128,546. Research studies in
                  Sjogren's syndrome and fibromyalgia syndrome represented
                  $1,095,840 of the accounts payable. Of this amount, $753,840
                  was paid in the first week of April.

                  The Company will need to raise additional funds to complete
                  the Sjogren's syndrome Phase 3 clinical trial. If these funds
                  are not obtained in the second quarter of this year the study
                  will be halted along with a reduction in staff and
                  administrative expenses. Management believes that based on the
                  Company's ability to curtail clinical trial expense and to
                  reduce staff and administrative expenses, available funds are
                  sufficient to meet anticipated cash requirements for the
                  remainder of 1999.

                  Discussions are presently underway to raise additional funds,
                  and the Company is also considering the possibility of a
                  strategic alliance with another biotech company.

                  SUBSEQUENT EVENTS

                  On April 2, 1999 the Company entered into an agreement whereby
                  two Promissory Notes totalling $2,600,000 plus accrued
                  interest of $237,526 owed to Hayashibara Biochemical
                  Laboratories ("Hayashibara") was converted into common stock.
                  The total number of shares issued to Hayashibara was 946,094
                  raising its total shares owned to 34.3% of the 6.36 million
                  shares outstanding. Prior to the conversion, total shares
                  outstanding were 5.41 million of which Hayashibara owned
                  22.8%. The value of the shares issued was based on the
                  weighted average sales price of the common stock for the ten
                  days prior to April 2nd and amounted to $2.9992 per share.



                                        7
<PAGE>   8

                           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
                  March 31, 1999.



                                        8
<PAGE>   9


                                   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:  May 14, 1999               By:  /s/ JOSEPH M. CUMMINS
                                     -------------------------------------------
                                           Joseph M. Cummins
                                           President, Chief Executive Officer
                                           and Chief Financial Officer



<PAGE>   10

                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
EXHIBIT NO.       DESCRIPTION
-----------       -----------
<S>               <C>
                  Exhibit 27.   Financial Data Schedule
</TABLE>