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

                                    FORM 10-Q
(MARK ONE)
              [X] 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 1-12380


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

                                  AVIALL, INC.
             (Exact name of Registrant as specified in its Charter)

                DELAWARE                                         65-0433083
     (State or other jurisdiction of                          (I.R.S. Employer
     incorporation or organization)                          Identification No.)

           2075 DIPLOMAT DRIVE
              DALLAS, TEXAS                                      75234-8999
(Address of principal executive offices)                         (Zip Code)

                                 (972) 406-2000
              (Registrant's telephone number, including area code)



     Indicate by check [X] 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 of Common Stock, par value $.01 per share, outstanding
at May 6, 1998 was 19,684,342.


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                         PART I - FINANCIAL INFORMATION



ITEM 1:  FINANCIAL STATEMENTS

                                  AVIALL, INC.
                        CONSOLIDATED STATEMENTS OF INCOME
                    (DOLLARS IN THOUSANDS, EXCEPT SHARE DATA)
                                   (UNAUDITED)



<TABLE>
<CAPTION>
                                                                                                    Three months ended
                                                                                                         March 31,
                                                                                              -----------------------------
                                                                                                  1998              1997
---------------------------------------------------------------------------------------------------------------------------
<S>                                                                                           <C>                    <C>   
Net sales                                                                                     $    98,030            91,682
Cost of sales                                                                                      72,990            68,638
---------------------------------------------------------------------------------------------------------------------------
Gross profit                                                                                       25,040            23,044
Operating and other expenses:
   Selling and administrative expenses                                                             17,187            16,191
   Nonrecurring items                                                                                  --            (1,436)
   Interest expense                                                                                   507               734
---------------------------------------------------------------------------------------------------------------------------
Earnings before income taxes                                                                        7,346             7,555
Provision for income taxes                                                                            367               612
---------------------------------------------------------------------------------------------------------------------------
Net earnings                                                                                  $     6,979             6,943
===========================================================================================================================

Basic net earnings per share                                                                  $      0.35              0.35
Weighted average common shares                                                                 19,968,503        19,576,555
===========================================================================================================================

Diluted net earnings per share                                                                $      0.34              0.35
Weighted average common and potentially dilutive common shares                                 20,388,350        19,714,638
===========================================================================================================================

</TABLE>




See accompanying notes to consolidated financial statements.




                                       2
<PAGE>   3



                                  AVIALL, INC.
                           CONSOLIDATED BALANCE SHEETS
                    (DOLLARS IN THOUSANDS, EXCEPT SHARE DATA)

<TABLE>
<CAPTION>
                                                                                          March 31,     December 31,
                                                                                             1998           1997
-------------------------------------------------------------------------------------------------------------------
                                                                                          (Unaudited)
<S>                                                                                         <C>               <C> 
ASSETS
Current assets:
   Cash                                                                                     $ 13,615          7,556
   Receivables                                                                                62,053         59,119
   Inventories                                                                                77,344         73,414
   Prepaid expenses and other current assets                                                   2,129          1,627
   Deferred income taxes                                                                      11,795         11,795
-------------------------------------------------------------------------------------------------------------------
Total current assets                                                                         166,936        153,511
-------------------------------------------------------------------------------------------------------------------

Property, plant and equipment                                                                 10,050          9,758
Intangible assets                                                                             54,581         55,134
Deferred income taxes                                                                         37,526         37,530
Other assets                                                                                   3,413          3,459
-------------------------------------------------------------------------------------------------------------------
Total assets                                                                                $272,506        259,392
===================================================================================================================

LIABILITIES AND SHAREHOLDERS' EQUITY 
Current liabilities:
   Current portion of long-term debt                                                        $ 11,070          8,556
   Accounts payable                                                                           33,502         27,765
   Accrued expenses                                                                           39,177         40,309
-------------------------------------------------------------------------------------------------------------------
Total current liabilities                                                                     83,749         76,630
-------------------------------------------------------------------------------------------------------------------

Long-term debt                                                                                25,001         28,004
Other liabilities                                                                             26,787         27,397
Shareholders' equity (includes common stock of $.01 par value per share with
   80,000,000 shares authorized; 20,128,590 shares and 19,900,195 shares issued
   at March 31, 1998 and at December 31, 1997, respectively; 20,115,490 shares
   and 19,900,195 shares outstanding at March 31, 1998 and at December 31, 1997,
   respectively; preferred stock of $.01 par value per share with 10,000,000 shares             
   authorized and no shares issued and outstanding)                                          136,969        127,361
-------------------------------------------------------------------------------------------------------------------
Total liabilities and shareholders' equity                                                  $272,506        259,392
===================================================================================================================

</TABLE>




See accompanying notes to consolidated financial statements.



                                       3

<PAGE>   4




                                  AVIALL, INC.
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                             (DOLLARS IN THOUSANDS)
                                   (UNAUDITED)


<TABLE>
<CAPTION>
                                                           Three months ended March 31,
                                                           ---------------------------
                                                              1998            1997
-------------------------------------------------------------------------------------
<S>                                                          <C>                <C>  
CASH FLOWS FROM OPERATING ACTIVITIES:
   Net earnings                                              $  6,979           6,943
   Nonrecurring items                                              --          (1,436)
   Depreciation and amortization                                1,376           1,375
   Compensation expense on restricted stock awards                 57              --
   Deferred income taxes                                            4               5
   Changes in:
     Receivables                                               (2,934)         (2,895)
     Inventories                                               (3,930)          1,596
     Accounts payable                                           5,737            (284)
     Accrued expenses                                          (1,132)         (5,029)
     Other, net                                                (1,067)         (1,079)
-------------------------------------------------------------------------------------
                                                                5,090            (804)
-------------------------------------------------------------------------------------
CASH FLOWS FROM INVESTING ACTIVITIES:
   Proceeds received from repayment of note receivable             --          12,000
   Capital expenditures                                        (1,033)           (136)
   Sales of property, plant and equipment                         (81)             67
-------------------------------------------------------------------------------------
                                                               (1,114)         11,931
-------------------------------------------------------------------------------------
CASH FLOWS FROM FINANCING ACTIVITIES:
   Debt repaid                                                 (2,272)        (12,253)
   Net change in revolving credit facility                      1,783           3,978
   Issuance of common stock                                     2,767             353
   Purchase of treasury stock                                    (195)             --
-------------------------------------------------------------------------------------
                                                                2,083          (7,922)
-------------------------------------------------------------------------------------
Change in cash                                                  6,059           3,205
Cash, beginning of period                                       7,556           4,191
-------------------------------------------------------------------------------------
Cash, end of period                                          $ 13,615           7,396
=====================================================================================
CASH PAID FOR INTEREST AND INCOME TAXES:
   Interest                                                  $    621           1,606
   Income taxes                                              $     78             513

</TABLE>




See accompanying notes to consolidated financial statements.




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                                  AVIALL, INC.
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS



NOTE 1 - BASIS OF PRESENTATION

     The accompanying unaudited financial statements have been prepared in
accordance with generally accepted accounting principles for interim financial
information and with the instructions to Form 10-Q and Article 10 of Regulation
S-X. Accordingly, these financial statements 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-month
period ended March 31, 1998 are not necessarily indicative of the results that
may be expected for the year ending December 31, 1998. For further information,
refer to the financial statements and footnotes thereto included in Aviall,
Inc.'s Form 10-K for the year ended December 31, 1997.




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<PAGE>   6



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

OVERVIEW. The following discussion and analysis should be read in conjunction
with the information set forth under Item 7: Management's Discussion and
Analysis of Financial Condition and Results of Operations on pages 13 through 19
of Aviall, Inc.'s (the "Company") Form 10K for the year ended December 31, 1997.

RESULTS OF OPERATIONS - THREE MONTHS ENDED MARCH 31, 1998 COMPARED TO THREE
MONTHS ENDED MARCH 31, 1997. Net sales for the first quarter of 1998 were $98.0
million, up $6.3 million, or 6.9%, from the $91.7 million recorded in the same
1997 quarter. Sales continued to grow in all major business segments and
geographic regions, although the European and Asian segments experienced slower
growth compared to recent quarters.

     Gross profit of $25.0 million was $2.0 million higher than the $23.0
million in the 1997 first quarter. Gross profit as a percentage of sales
increased from 25.1% to 25.5%. This increase in gross profit percentage was
primarily a result of increased volume in product repair service locations and
fewer special incentive programs.

     Selling and administrative expenses increased $1.0 million or 6.2% to $17.2
million in the first quarter of 1998. The increase primarily resulted from
higher commission payments and freight expense, and costs for the implementation
of new information systems and the Company's exhibit at the biennial Singapore
Air Show.

     Interest expense was lower than in the first quarter 1997, reflecting lower
debt, lower interest rates from the 1996 bank agreement and higher interest
income from the larger cash balance.

     The 1997 results include a $1.4 million nonrecurring gain from the full
repayment in January 1997 of a discounted note received in connection with the
1995 sale of the business aviation engine overhaul, and aircraft and terminal
services operations.

FINANCIAL CONDITION. Cash flows from operations were $5.1 million in the first
three months of 1998 and $(0.8) million in the comparable 1997 period. The
improved cash flow was due to the lower payments related to liabilities retained
for previously owned businesses and higher accounts payable primarily related to
an increase in inventory in the first quarter of 1998.

     In January 1998, the Company's Board of Directors authorized a $30 million
share repurchase program to buyback up to 10% of the Company's outstanding
common stock over the next two years in open market transactions, depending on
market, economic and other factors. The Company intends to use existing cash
balances and future cash flows to fund this program. As of May 6, 1998, the
Company has purchased a total of 454,200 shares for $6.7 million. Management
does not expect the share repurchase program to restrict the Company from
pursuing other opportunities for growth.

     In January 1997, a $12.0 million unsecured subordinated note received in
connection with the 1995 sale of the business aviation engine repair operation
was repaid in full. The Company applied the proceeds as a permanent reduction of
the term loan under its existing credit agreement. Because of the uncertainty
regarding the collection of the note when it was received in March 1995, the
Company carried the note at a discounted value of $10.5 million.

     The Company's income tax expense continues to be substantially lower than
the U.S. federal statutory rate due to the utilization of the U.S. net operating
loss ("NOL") carryforward and the corresponding decrease in the valuation
allowance on the deferred tax assets. The Company's tax expense is primarily
related to foreign taxes on foreign operations. For U.S. federal tax purposes as
of December 31, 1997, the Company had an estimated NOL carryforward of
approximately $200 million, substantially expiring in 2009-2011, which will
minimize U.S. federal income tax cash payments for several years. If certain
substantial changes in the Company's ownership should occur, there would be an
annual limitation on the amount of the NOL carryforward that could be utilized.

     The Company believes that its expected cash flow from operations and
availability under its revolving lines of credit are sufficient to meet its
current working capital and operating needs as well as implement the share
repurchase program announced in January 1998. Improvements in earnings will
further enhance the Company's access to capital and will enable the Company to
finance future investment opportunities.




                                       6
<PAGE>   7




OUTLOOK. The Company is in the process of replacing its financial and parts
distribution operating systems with planned implementation dates of second
quarter and fourth quarter of 1998, respectively. The financial system's first
phase was implemented on schedule. These new systems are Year 2000 compliant.
The Company has retained a consultant to conduct a Year 2000 hardware review
with recommendations to be implemented by year end 1998. Based on the
implementation and assessment dates, management believes implementation will be
completed in a timely manner and there will be no material effect on its future
financial results in order to bring the Company's systems Year 2000 compliant.

     The Company's financial and parts distribution operating systems are
critical to Aviall's success. Implementation of complex new software systems
carries certain risks that may affect normal operations for a period of time.
Management believes their implementation process and strategy combined with
appropriate training throughout the organization will minimize these risks.

     Aviall primarily participates in the global aviation aftermarket through
its core aviation parts distribution and inventory information services
businesses. The Company can be affected by the general economic cycle,
particularly as it influences flight activity in commercial, business and
general aviation. Recent favorable economic conditions have led to an improved
aviation market, and provided the Company with the opportunity for growth.

     The Company serves a significant number of customers in the Asia-Pacific
and Latin America regions. Recent events, particularly in the Asia-Pacific
region, have increased financial volatility and currency fluctuations relative
to the U.S. dollar. These factors have depressed air travel which impacts
customers' need for aircraft parts and potentially their ability to pay in a
timely manner. The Company continues to closely monitor these events.

CERTAIN FORWARD-LOOKING STATEMENTS. This report contains certain forward-looking
statements (as such term is defined in the Private Securities Litigation Reform
Act of 1995) relating to the Company that are based on the beliefs of the
management of the Company, as well as assumptions and estimates made by and
information currently available to the Company's management. When used in this
report, the words "anticipate," "believe," "estimate," "expect," "intend" and
similar expressions, as they relate to the Company or the Company's management,
identify forward-looking statements. Such statements reflect the current views
of the Company with respect to future events and are subject to certain risks,
uncertainties and assumptions relating to the operations and results of
operations of the Company as well as its customers and suppliers, including as a
result of competitive factors and pricing pressures, shifts in market demand,
general economic conditions and other factors including among others, those that
effect flight activity in commercial, business and general aviation, the
business activities of the Company's customers and suppliers and developments in
information and communication technology. Should one or more of these risks or
uncertainties materialize, or should underlying assumptions or estimates prove
incorrect, actual results may vary materially from those described herein as
anticipated, believed, estimated, expected or intended.

                           PART II - OTHER INFORMATION

ITEM 6:  EXHIBITS AND REPORTS ON FORM 8-K

     (a)  Exhibits

          27.1     Financial Data Schedule

     (b)  Reports on Form 8-K

          No reports on Form 8-K have been filed during the quarter for which
this report is filed.




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<PAGE>   8




                                   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 by the
undersigned thereunto duly authorized.

                                       AVIALL, INC.


May 11, 1998                            By   /s/ Jacqueline K. Collier
                                             -----------------------------------
                                             Jacqueline K. Collier
                                             Vice President and Controller


May 11, 1998                                 /s/ Cornelius Van Den Handel
                                             -----------------------------------
                                             Cornelius Van Den Handel
                                             Vice President and Treasurer
                                             (Principal Financial Officer)




                                       8


<PAGE>   9



                                INDEX TO EXHIBITS

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