<PAGE>   1
                                  UNITED STATES

                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

                                    FORM 10-Q

[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               1-7077

                           GTE SOUTHWEST INCORPORATED
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)

                DELAWARE                                 75-0573444
    (STATE OR OTHER JURISDICTION OF         (I.R.S. EMPLOYER IDENTIFICATION NO.)
     INCORPORATION OR ORGANIZATION)

600 Hidden Ridge, HQE04B12 - Irving, Texas                  75038
 (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)                 (ZIP CODE)

Registrant's telephone number, including area code       972-718-5600


              (Former name, former address and former fiscal year,
                         if changed since last report)




Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.

                                                              YES [X]   NO [ ]

The Company had 6,500,000 shares of $100 stated value common stock outstanding
at April 30, 1998. The Company's common stock is 100% owned by GTE Corporation.


<PAGE>   2

PART I.  FINANCIAL INFORMATION

GTE Southwest Incorporated
CONDENSED STATEMENTS OF INCOME

<TABLE>
<CAPTION>
                                                                       Three Months Ended
                                                                           March 31,
                                                                 ----------------------------
                                                                    1998              1997
                                                                 -----------      -----------
                                                                    (Thousands of Dollars)
<S>                                                              <C>              <C>        
REVENUES AND SALES
   Local services                                                $   174,199      $   158,731
   Network access services                                           166,042          158,421
   Toll services                                                      24,772           40,624
   Other services and sales                                           58,985           59,928
                                                                 -----------      -----------

     Total revenues and sales                                        423,998          417,704
                                                                 -----------      -----------

OPERATING COSTS AND EXPENSES
   Cost of services and sales                                        161,667          129,012
   Selling, general and administrative                                67,551           50,451
   Depreciation and amortization                                      92,528           93,054
                                                                 -----------      -----------

     Total operating costs and expenses                              321,746          272,517
                                                                 -----------      -----------

OPERATING INCOME                                                     102,252          145,187
   Interest - net                                                     16,555           14,504
                                                                 -----------      -----------

INCOME BEFORE INCOME TAXES                                            85,697          130,683
   Income taxes                                                       29,658           44,254
                                                                 -----------      -----------

INCOME BEFORE EXTRAORDINARY CHARGE                                    56,039           86,429
   Extraordinary charge                                                 (462)              --
                                                                 -----------      -----------

NET INCOME                                                       $    55,577      $    86,429
                                                                 ===========      ===========
</TABLE>




Per share data is omitted since the Company's common stock is 100% owned by GTE
Corporation (GTE).

See Notes to Condensed Financial Statements.



                                       1
<PAGE>   3

GTE Southwest Incorporated

MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
AND RESULTS OF OPERATIONS

(Dollars in Millions)

RESULTS OF OPERATIONS

<TABLE>
<CAPTION>
                                                                     Three Months Ended
                                                                           March 31,
                                                                 -----------------------------
                                                                     1998             1997
                                                                 ------------     ------------
<S>                                                              <C>              <C>         
         Net income                                              $       55.6     $       86.4
</TABLE>

Net income for the three months ended March 31, 1998 includes an after-tax
extraordinary charge of $0.5. Excluding this charge, net income decreased 35% or
$30.3 for the three months ended March 31, 1998, compared to the same period in
1997. The decline in net income is primarily due to higher operating costs and
expenses, partially offset by an increase in revenues and sales.

REVENUES AND SALES

<TABLE>
<CAPTION>
                                                                     Three Months Ended
                                                                          March 31,
                                                                 ---------------------------
                                                                    1998            1997
                                                                 -----------     -----------
<S>                                                              <C>             <C>        
         Local services                                          $     174.2     $     158.8
         Network access services                                       166.0           158.4
         Toll services                                                  24.8            40.6
         Other services and sales                                       59.0            59.9
                                                                 -----------     -----------

           Total revenues and sales                              $     424.0     $     417.7
</TABLE>

Total revenues and sales increased 2% or $6.3 for the three months ended March
31, 1998, compared to the same period in 1997.

Local service revenues increased 10% or $15.4 for the three months ended March
31, 1998, compared to the same period in 1997. The number of access lines
increased 7% which generated additional revenues of $4 from basic local
services, $2.1 from CentraNet(R) services and $2.5 from Integrated Services
Digital Network (ISDN) and Digital Channel Services (DCS). In addition, revenues
from enhanced services, such as caller ID, automatic call return/redial and
other SmartCall(R) and CLASS services, contributed $3.2 to the increase.

Network access service revenues increased 5% or $7.6 for the three months ended
March 31, 1998, compared to the same period in 1997. Increased demand for access
services by interexchange carriers resulted in a 12% growth in minutes of use
which generated $12.4 of additional revenues. Special access revenues, driven by
growing demand for increased bandwidth services by Internet Service Providers
(ISPs) and other high capacity users, increased by $5.8 and an increase in the
volume of cellular service providers accessing the Company's network generated
additional revenues of $2.7. These increases were partially offset by a $7.3
decrease resulting from interstate access rate reductions associated with the
1997 Federal Communications Commission (FCC) price cap. The results also reflect
a decline of $10.4 resulting from the sharing provisions of the FCC's 1996 and
1997 price caps recorded in the first quarter of 1998, partially offset by
reserves of $1.4 which were established in the first quarter of 1997.



                                       2
<PAGE>   4

MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
AND RESULTS OF OPERATIONS (CONTINUED)

Toll service revenues decreased 39% or $15.8 for the three months ended March
31, 1998, compared to the same period in 1997. The decrease is primarily due to
reduced toll volumes resulting from the effects of intraLATA (local access
transport area) toll competition, including 10XXX and 1+ presubscription.

OPERATING COSTS AND EXPENSES

<TABLE>
<CAPTION>
                                                                     Three Months Ended
                                                                          March 31,
                                                                 ---------------------------
                                                                    1998            1997
                                                                 -----------     -----------
<S>                                                              <C>             <C>        
         Total operating costs and expenses                      $     321.7     $     272.5
</TABLE>

Total operating costs and expenses increased 18% or $49.2 for the three months
ended March 31, 1998, compared to the same period in 1997. This increase is due
in part to higher labor and benefit costs of $16.9 and an increase in Info Page
billings from directory publications of $4.6. Selling and marketing expenses
increased $5 during the three month period as a result of continued efforts to
stimulate sales of enhanced services and in response to the increasingly
competitive environment. The results also reflect the impact of a $13.7
settlement gain recorded in the first quarter of 1997, which resulted from lump
sum payments from the Company's pension plans. These increases were slightly 
offset by a $1.8 decline in access charges incurred to terminate customers' 
intraLATA toll calls outside the Company's service territories.

OTHER EXPENSES

<TABLE>
<CAPTION>
                                                                     Three Months Ended
                                                                          March 31,
                                                                 ---------------------------
                                                                    1998            1997
                                                                 -----------     -----------
<S>                                                              <C>             <C>        
         Interest - net                                          $      16.6     $      14.5
         Income taxes                                                   29.7            44.3
         Extraordinary charge                                            0.5              --
</TABLE>

Interest - net increased 14% or $2.1 for the three months ended March 31, 1998,
compared to the same period in 1997. This increase is primarily due to higher
average short-term debt levels.

Income taxes decreased 33% or $14.6 for the three months ended March 31, 1998,
compared to the same period in 1997. This decline is primarily due to a
corresponding decrease in pre-tax income, partially offset by other tax
adjustments.

During the first quarter of 1998, the Company recorded an after-tax
extraordinary charge of $0.5, reflecting premiums paid on the redemption of
high-coupon debt prior to stated maturity.



                                       3
<PAGE>   5

MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
AND RESULTS OF OPERATIONS (CONTINUED)

CAPITAL RESOURCES AND LIQUIDITY

Management believes the Company has adequate internal and external resources
available to meet ongoing operating requirements for construction of new plant,
modernization of facilities and payment of dividends. The Company generally
funds its construction program from operations, although external financing is
available. Short-term financings can be obtained through borrowings from the
Company's parent, GTE, or GTE Funding Incorporated, an affiliate of the Company.
The Company participates with other affiliates in a $1,500, 364-day syndicated
line of credit. In December 1997, the Company began participating with GTE and
other of its affiliates in a series of five bilateral credit agreements for an
additional $2,000 in credit capacity. These facilities, which are shared by the
participating companies, are aligned with the maturity date of the existing
364-day line of credit.

The Company's primary source of funds during the first three months of 1998 was
cash from operations of $182 compared to $190.8 for the same period in 1997. The
year-to-year decrease is primarily attributable to a decline in results from
operations and an increase in working capital requirements.

The Company's capital expenditures during the first three months of 1998 were
$118 compared to $80.6 for the same period in 1997. The 1998 expenditures
reflect the Company's continued growth in primary and secondary access lines and
the modernization of interoffice facilities to mitigate Internet congestion.
Although the capital expenditures during the first three months of 1998 were
higher than the same period in 1997, the overall anticipated capital
expenditures for 1998 are expected to be comparable to the total capital
expenditures incurred during 1997.

Net cash used in financing activities was $64.4 for the three months ended March
31, 1998, compared to $92.2 for the same period in 1997. This included dividend
payments of $45.5 for the first three months of 1998, compared to $49.8 for the
same period in 1997. Short-term financings, including the net change in
affiliate notes, decreased $123.2 in the first quarter of 1998, compared to a
decrease of $42.4 for the same period in 1997. In January 1998, the Company
issued $150 of 6.23% debentures to repay short-term borrowings incurred to
finance the Company's construction program and for general corporate purposes.
The Company also retired $42 of long-term debt and preferred stock during the
first quarter of 1998, which included $0.5 in premiums paid to retire the debt
and redeem the preferred stock prior to stated maturity.

In its April 2, 1998 filing on Form 8-K, the Company's parent, GTE, stated that
because the MCI shareholders had accepted a competing offer, GTE's offer for MCI
was no longer outstanding. As a result, the Company and GTE were removed from
"Credit Watch" by all rating agencies. The Company believes that its present
investment grade credit rating provides ready access to the capital markets at
reasonable rates and provides the Company with the financial flexibility
necessary to pursue growth opportunities as they arise.

RECENT DEVELOPMENTS

In April 1998, the Company's parent, GTE, announced a series of actions designed
to further sharpen its strategic focus and improve its competitive position by
repositioning non-strategic properties and reducing costs. GTE expects to
generate after-tax proceeds of $2,000 - $3,000 by selling non-strategic or
under-performing operations, and plans to reduce annual costs by more than $500
through improved efficiencies and productivity while it continues to invest in
new high-growth opportunities. The impact of this announcement on the Company is
unknown at this time. GTE's management is currently assessing its options and,
as decisions are finalized regarding the sale of non-strategic operations and
cost reductions, the Company could be affected.



                                       4
<PAGE>   6

GTE Southwest Incorporated
CONDENSED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                                        March 31,         December 31,
                                                                          1998                1997
                                                                      -------------      -------------
                                                                           (Thousands of Dollars)
<S>                                                                   <C>                <C>          
ASSETS
Current assets:
  Cash and cash equivalents                                           $      23,796      $      24,282
  Receivables, less allowances of $20,681 and $21,203                       311,643            359,879
  Inventories and supplies                                                   47,519             24,032
  Prepaid insurance                                                          22,951              1,587
  Prepaid taxes and other                                                    12,634             58,379
                                                                      -------------      -------------

    Total current assets                                                    418,543            468,159
                                                                      -------------      -------------

Property, plant and equipment, at cost                                    5,523,114          5,418,247
  Accumulated depreciation                                               (3,395,216)        (3,317,186)
                                                                      -------------      -------------

    Total property, plant and equipment, net                              2,127,898          2,101,061

Prepaid pension costs and other assets                                      177,252            162,995
                                                                      -------------      -------------

Total assets                                                          $   2,723,693      $   2,732,215
                                                                      =============      =============

LIABILITIES AND SHAREHOLDERS' EQUITY
Current liabilities:
  Short-term obligations, including current maturities                $         313      $         313
  Notes payable to affiliates                                                84,812             42,826
  Accounts payable                                                          166,056            204,648
  Taxes payable                                                              16,030             37,027
  Accrued interest                                                           18,339             10,103
  Accrued payroll costs                                                      43,487             33,252
  Dividends payable                                                          34,766             45,458
  Other                                                                     126,936            106,267
                                                                      -------------      -------------

    Total current liabilities                                               490,739            479,894
                                                                      -------------      -------------

  Long-term debt                                                            942,650            984,955
  Deferred income taxes                                                     174,563            174,745
  Employee benefit plans and other liabilities                              242,436            238,556
                                                                      -------------      -------------

    Total liabilities                                                     1,850,388          1,878,150
                                                                      -------------      -------------

Preferred stock, subject to mandatory redemption                                 --              1,510
                                                                      -------------      -------------

Shareholders' equity:
  Preferred stock                                                             7,600              7,600
  Common stock (6,500,000 shares issued)                                    650,000            650,000
  Additional paid-in capital                                                 48,751             48,751
  Retained earnings                                                         166,954            146,204
                                                                      -------------      -------------

    Total shareholders' equity                                              873,305            852,555
                                                                      -------------      -------------

Total liabilities and shareholders' equity                            $   2,723,693      $   2,732,215
                                                                      =============      =============
</TABLE>


See Notes to Condensed Financial Statements.



                                       5
<PAGE>   7

GTE Southwest Incorporated
CONDENSED STATEMENTS OF CASH FLOWS

<TABLE>
<CAPTION>
                                                                                               Three Months Ended
                                                                                                   March 31,
                                                                                          ----------------------------
                                                                                             1998             1997
                                                                                          -----------      -----------
                                                                                             (Thousands of Dollars)
<S>                                                                                       <C>              <C>        
OPERATIONS
  Income before extraordinary charge                                                      $    56,039      $    86,429
  Adjustments to reconcile income before extraordinary charge to net cash from
  operations:
    Depreciation and amortization                                                              92,528           93,054
    Deferred income taxes                                                                       2,280            1,459
    Provision for uncollectible accounts                                                        8,486            7,534
    Changes in current assets and current liabilities                                          18,398           23,666
    Other - net                                                                                 4,264          (21,316)
                                                                                          -----------      -----------

    Net cash from operations                                                                  181,995          190,826
                                                                                          -----------      -----------

INVESTING
  Capital expenditures                                                                       (118,040)         (80,571)
                                                                                          -----------      -----------

    Cash used in investing                                                                   (118,040)         (80,571)
                                                                                          -----------      -----------

FINANCING
  Long-term debt issued                                                                       148,868               --
  Long-term debt and preferred stock retired, including premiums
      paid on early retirement                                                                (42,013)             (95)
  Dividends                                                                                   (45,481)         (49,790)
  Decrease in short-term obligations, excluding
      current maturities                                                                     (123,179)         (42,353)
  Other - net                                                                                  (2,636)              --
                                                                                          -----------      -----------

    Net cash used in financing                                                                (64,441)         (92,238)
                                                                                          -----------      -----------

Increase (decrease) in cash and cash equivalents                                                 (486)          18,017

Cash and cash equivalents:
  Beginning of period                                                                          24,282           23,134
                                                                                          -----------      -----------

  End of period                                                                           $    23,796      $    41,151
                                                                                          ===========      ===========
</TABLE>



See Notes to Condensed Financial Statements.


                                       6
<PAGE>   8

GTE Southwest Incorporated
NOTES TO CONDENSED FINANCIAL STATEMENTS

(1)      BASIS OF PRESENTATION:

         The unaudited condensed financial statements included herein have been
         prepared by the Company pursuant to the rules and regulations of the
         Securities and Exchange Commission. Certain information and footnote
         disclosures normally included in financial statements prepared in
         accordance with generally accepted accounting principles have been
         condensed or omitted pursuant to such rules and regulations. However,
         in the opinion of management of the Company, the condensed financial
         statements include all adjustments, which consist only of normal
         recurring accruals, necessary to present fairly the financial
         information for such periods. These condensed financial statements
         should be read in conjunction with the financial statements and the
         notes thereto included in the Company's 1997 Annual Report on Form
         10-K.

         Reclassifications of prior year data have been made, where appropriate,
         to conform to the 1998 presentation.

(2)      EXTRAORDINARY CHARGE:

         During the first quarter of 1998, the Company recorded an after-tax
         extraordinary charge of $0.5 million, reflecting premiums paid on the
         redemption of high-coupon debt prior to stated maturity.

(3)      RECENT ACCOUNTING PRONOUNCEMENT:

         In March 1998, the American Institute of Certified Public Accountants
         issued Statement of Position 98-1, "Accounting for the Costs of
         Computer Software Developed or Obtained for Internal Use" (SOP 98-1).
         SOP 98-1 defines internal-use software and establishes accounting
         standards for the costs of such software. The Company is currently
         assessing the impact of adopting SOP 98-1.



                                       7
<PAGE>   9

GTE Southwest Incorporated
PART II.  OTHER INFORMATION

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

    (a)  Exhibits required by Item 601 of Regulation S-K.

         12 Statement re: Calculation of the Ratio of Earnings to Fixed Charges

         27 Financial Data Schedule

    (b)  The Company filed a report on Form 8-K, dated January 5, 1998, under
         Item 7 "Financial Statements and Exhibits." No financial statements
         were filed with this report.





                                       8
<PAGE>   10

                                    SIGNATURE

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.



                                          GTE Southwest Incorporated
                                  ----------------------------------------
                                                (Registrant)



Date:    May 15, 1998                       /s/ Stephen L. Shore
     -------------------          ----------------------------------------
                                                Stephen L. Shore

                                                   Controller
                                        (Principal Accounting Officer)




                                       9
<PAGE>   11

EXHIBIT INDEX

<TABLE>
<CAPTION>
     Exhibit
      Number                                                     Description
-------------------        -----------------------------------------------------------------------------------------
<S>                        <C>
        12                 Statement re: Calculation of the Ratio of Earnings to Fixed Charges

        27                 Financial Data Schedule
</TABLE>