<PAGE>   1
                       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 0-17687
                                                -------

Enstar Income/Growth Program Six-A, L.P.
--------------------------------------------------------------------------------
             (Exact name of Registrant as specified in its charter)

           Georgia                                             58-1755230
-------------------------------                          -----------------------
(State or other jurisdiction of                             (I.R.S. Employer
 incorporation or organization)                          Identification Number)


10900 Wilshire Boulevard - 15th Floor
    Los Angeles, California                                      90024
----------------------------------------                 -----------------------
(Address of principal executive offices)                       (Zip Code)

Registrant's telephone number, including area code:   (310) 824-9990
                                                   --------------------


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

<PAGE>   2

                         PART I - FINANCIAL INFORMATION

                    ENSTAR INCOME/GROWTH PROGRAM SIX-A, L.P.

                            CONDENSED BALANCE SHEETS

                    ========================================



<TABLE>
<CAPTION>
                                                                         December 31,           March 31,
                                                                            1997*                 1998
                                                                         -----------          -----------
                                                                                              (Unaudited)
<S>                                                                      <C>                  <C>        
ASSETS:
   Cash and cash equivalents                                             $   659,400          $   840,100

   Accounts receivable, less allowance of $5,400 and
      $2,900 for possible losses                                              20,000               46,600

   Prepaid expenses and other assets                                          38,200               49,100

   Property, plant and equipment, less accumulated
      depreciation and amortization of $4,896,400 and $5,002,900           3,428,900            3,300,300

   Franchise cost, net of accumulated
      amortization of $2,500,900 and $2,564,300                            1,141,500            1,083,000

   Deferred loan costs and other charges, net                                 71,000               66,600
                                                                         -----------          -----------

                                                                         $ 5,359,000          $ 5,385,700
                                                                         ===========          ===========

                                   LIABILITIES AND PARTNERSHIP CAPITAL
                                   -----------------------------------

LIABILITIES:
   Accounts payable                                                      $   460,200          $   376,900
   Due to affiliates                                                         507,200              496,500
   Note payable - affiliate                                                2,500,000            2,500,000
                                                                         -----------          -----------

              TOTAL LIABILITIES                                            3,467,400            3,373,400
                                                                         -----------          -----------

COMMITMENTS AND CONTINGENCIES

PARTNERSHIP CAPITAL (DEFICIT):
   General partners                                                         (143,700)            (142,500)
   Limited partners                                                        2,035,300            2,154,800
                                                                         -----------          -----------

              TOTAL PARTNERSHIP CAPITAL                                    1,891,600            2,012,300
                                                                         -----------          -----------

                                                                         $ 5,359,000          $ 5,385,700
                                                                         ===========          ===========
</TABLE>



               *As presented in the audited financial statements.
            See accompanying notes to condensed financial statements.



                                      -2-
<PAGE>   3

                    ENSTAR INCOME/GROWTH PROGRAM SIX-A, L.P.

                       CONDENSED STATEMENTS OF OPERATIONS

                    ========================================



<TABLE>
<CAPTION>
                                                          Unaudited
                                                 ----------------------------
                                                       Three months ended
                                                           March 31,
                                                 ----------------------------
                                                    1997               1998
                                                 ---------          ---------
<S>                                              <C>                <C>      
REVENUES                                         $ 905,800          $ 923,600
                                                 ---------          ---------

OPERATING EXPENSES:
   Service costs                                   299,000            301,900
   General and administrative expenses             102,000            108,500
   General Partner management fees
      and reimbursed expenses                      131,200            130,000
   Depreciation and amortization                   248,900            209,600
                                                 ---------          ---------

                                                   781,100            750,000
                                                 ---------          ---------

OPERATING INCOME                                   124,700            173,600
                                                 ---------          ---------

OTHER INCOME (EXPENSE):
   Interest income                                   2,800              7,700
   Interest expense                                (61,200)           (60,600)
   Gain on sale of cable assets                        100               --
                                                 ---------          ---------

                                                   (58,300)           (52,900)
                                                 ---------          ---------

NET INCOME                                       $  66,400          $ 120,700
                                                 =========          =========

Net income allocated to General Partners         $     700          $   1,200
                                                 =========          =========

Net income allocated to Limited Partners         $  65,700          $ 119,500
                                                 =========          =========

NET INCOME PER UNIT OF LIMITED
   PARTNERSHIP INTEREST                          $     .82          $    1.50
                                                 =========          =========

AVERAGE LIMITED PARTNERSHIP
   UNITS OUTSTANDING DURING PERIOD                  79,818             79,818
                                                 =========          =========
</TABLE>



            See accompanying notes to condensed financial statements.



                                      -3-
<PAGE>   4

                    ENSTAR INCOME/GROWTH PROGRAM SIX-A, L.P.

                            STATEMENTS OF CASH FLOWS

                    ========================================


<TABLE>
<CAPTION>
                                                                                     Unaudited
                                                                           ----------------------------
                                                                                 Three months ended
                                                                                     March 31,
                                                                           ----------------------------
                                                                             1997                1998
                                                                           ---------          ---------
<S>                                                                        <C>                <C>      
CASH FLOWS FROM OPERATING ACTIVITIES:
   Net income                                                              $  66,400          $ 120,700
   Adjustments to reconcile net income to net cash
      provided by operating activities:
         Depreciation and amortization                                       248,900            209,600
         Amortization of deferred loan costs                                   3,800              4,200
         Gain on sale of cable assets                                           (100)             --
         Decrease from changes in:
            Accounts receivable, prepaid expenses and other assets            (6,100)           (37,500)
            Accounts payable                                                (108,100)           (83,300)
                                                                           ---------          ---------

                 Net cash provided by operating activities                   204,800            213,700
                                                                           ---------          ---------

CASH FLOWS FROM INVESTING ACTIVITIES:
   Capital expenditures                                                      (23,300)           (15,400)
   Increase in intangible assets                                             (10,300)            (6,000)
   Proceeds from sale of property, plant and equipment                           100              --
                                                                           ---------          ---------

                 Net cash used in investing activities                       (33,500)           (21,400)
                                                                           ---------          ---------

CASH FLOWS FROM FINANCING ACTIVITIES:
   Due to affiliates                                                           6,400            (10,700)
   Deferred loan costs                                                          (300)              (900)
   Repayment of debt                                                        (300,000)             --
                                                                           ---------          ---------

                 Net cash used in financing activities                      (293,900)           (11,600)
                                                                           ---------          ---------

INCREASE (DECREASE) IN CASH AND
   CASH EQUIVALENTS                                                         (122,600)           180,700

CASH AND CASH EQUIVALENTS
   AT BEGINNING OF PERIOD                                                    169,400            659,400
                                                                           ---------          ---------

CASH AND CASH EQUIVALENTS
   AT END OF PERIOD                                                        $  46,800          $ 840,100
                                                                           =========          =========
</TABLE>



            See accompanying notes to condensed financial statements.



                                      -4-
<PAGE>   5

                    ENSTAR INCOME/GROWTH PROGRAM SIX-A, L.P.

                     NOTES TO CONDENSED FINANCIAL STATEMENTS

                    ========================================

1.          INTERIM FINANCIAL STATEMENTS

            The accompanying condensed interim financial statements for the
three months ended March 31, 1998 and 1997 are unaudited. These condensed
interim financial statements should be read in conjunction with the audited
financial statements and notes thereto included in the Partnership's latest
Annual Report on Form 10-K. In the opinion of management, such statements
reflect all adjustments (consisting only of normal recurring adjustments)
necessary for a fair presentation of the results of such periods. The results of
operations for the three months ended March 31, 1998 are not necessarily
indicative of results for the entire year.

2.          TRANSACTIONS WITH THE GENERAL PARTNERS AND AFFILIATES

            The Partnership has a management and service agreement with a wholly
owned subsidiary of the Corporate General Partner (the "Manager") for a monthly
management fee of 5% of revenues, excluding revenues from the sale of cable
television systems or franchises. Management fee expense approximated $46,200
for the three months ended March 31, 1998.

            In addition to the monthly management fee described above, the
Partnership reimburses the Manager for direct expenses incurred on behalf of the
Partnership and for the Partnership's allocable share of operational costs
associated with services provided by the Manager. All cable television
properties managed by the Corporate General Partner and its subsidiary are
charged a proportionate share of these expenses. The Corporate General Partner
has contracted with Falcon Holding Group, L.P. ("FHGLP"), an affiliated
partnership, to provide corporate management services for the Partnership.
Corporate office allocations and district office expenses are charged to the
properties served based primarily on the respective percentage of basic
subscribers or homes passed (dwelling units within a system) within the
designated service areas. The total amount charged to the Partnership for these
services approximated $83,800 for the three months ended March 31, 1998.
Management fees and reimbursed expenses due the Corporate General Partner are
non-interest bearing.

            The Partnership also receives certain system operating management
services from an affiliate of the Corporate General Partner in addition to the
Manager due to the fact that there are no such employees directly employed by
one of the Partnership's cable systems. The Partnership reimburses the affiliate
for its allocable share of the affiliate's operational costs. The total amount
charged to the Partnership for these costs approximated $4,100 for the three
months ended March 31, 1998. No management fee is payable to the affiliate by
the Partnership and there is no duplication of reimbursed expenses and costs
paid to the Manager.

            Certain programming services have been purchased through an
affiliate of the Partnership. In turn, the affiliate charges the Partnership for
these costs based on an estimate of what the Corporate General Partner could
negotiate for such programming services for the 15 partnerships managed by the
Corporate General Partner as a group. The Partnership recorded programming fee
expense of $198,700 for the three months ended March 31, 1998. Programming fees
are included in service costs in the statements of operations.



                                      -5-
<PAGE>   6


                    ENSTAR INCOME/GROWTH PROGRAM SIX-A, L.P.

                     NOTES TO CONDENSED FINANCIAL STATEMENTS

                    ========================================



3.          EARNINGS PER UNIT OF LIMITED PARTNERSHIP INTEREST

            Earnings and losses per unit of limited partnership interest is
based on the average number of units outstanding during the periods presented.
For this purpose, earnings and losses have been allocated 99% to the Limited
Partners and 1% to the General Partners. The General Partners do not own units
of partnership interest in the Partnership, but rather hold a participation
interest in the income, losses and distributions of the Partnership.






                                      -6-


<PAGE>   7

                    ENSTAR INCOME/GROWTH PROGRAM SIX-A, L.P.


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

INTRODUCTION

            The Cable Television Consumer Protection and Competition Act of 1992
(the "1992 Cable Act") required the Federal Communications Commission ("FCC")
to, among other things, implement extensive regulation of the rates charged by
cable television systems for basic and programming service tiers, installation,
and customer premises equipment leasing. Compliance with those rate regulations
has had a negative impact on the Partnership's revenues and cash flow. The
Telecommunications Act of 1996 (the "1996 Telecom Act") substantially changed
the competitive and regulatory environment for cable television and
telecommunications service providers. Among other changes, the 1996 Telecom Act
provides that the regulation of cable programming service tier ("CPST") rates
will be terminated on March 31, 1999. Because cable service rate increases have
continued to outpace inflation under the FCC's existing regulations, the
Partnership expects Congress and the FCC to explore additional methods of
regulating cable service rate increases, including deferral or repeal of the
March 31, 1999 termination of CPST rate regulation. There can be no assurance as
to what, if any, further action may be taken by the FCC, Congress or any other
regulatory authority or court, or the effect thereof on the Partnership's
business. Accordingly, the Partnership's historical financial results as
described below are not necessarily indicative of future performance.

            This Report includes certain forward looking statements regarding,
among other things, future results of operations, regulatory requirements,
competition, capital needs and general business conditions applicable to the
Partnership. Such forward looking statements involve risks and uncertainties
including, without limitation, the uncertainty of legislative and regulatory
changes and the rapid developments in the competitive environment facing cable
television operators such as the Partnership. In addition to the information
provided herein, reference is made to the Partnership's Annual Report on Form
10-K for the year ended December 31, 1997 for additional information regarding
such matters and the effect thereof on the Partnership's business.

RESULTS OF OPERATIONS

            The Partnership's revenues increased from $905,800 to $923,600, or
by 2.0%, for the three months ended March 31, 1998 as compared to the
corresponding period in 1997. Of the $17,800 increase, $45,600 was due to
increases in regulated service rates that were implemented by the Partnership in
1997 and $1,800 was due to increases in other revenue producing items. These
increases were partially offset by a decrease of $29,600 due to decreases in the
number of subscriptions for basic, tier and equipment rental services. As of
March 31, 1998, the Partnership had approximately 9,300 basic subscribers and
2,400 premium service units.

            Service costs increased from $299,000 to $301,900, or by 1.0%, for
the three months ended March 31, 1998 as compared to the corresponding period in
1997. Service costs represent costs directly attributable to providing cable
services to customers. The increase was primarily due to decreased
capitalization of labor and overhead costs resulting from fewer capital projects
in the first three months of 1998 and due to higher programming expense.
Programming expense increased primarily as a result of higher rates charged by
program suppliers.




                                      -7-
<PAGE>   8

                    ENSTAR INCOME/GROWTH PROGRAM SIX-A, L.P.


RESULTS OF OPERATIONS (CONTINUED)

            General and administrative expenses increased from $102,000 to
$108,500, or by 6.4%, for the three months ended March 31, 1998 as compared to
the corresponding period in 1997. The increase was primarily due to higher
marketing and telephone expenses.

            Management fees and reimbursed expenses remained relatively
unchanged, decreasing from $131,200 to $130,000 (less than one percent), for the
quarter ended March 31, 1998 as compared to the corresponding period in 1997.
Management fees increased in direct relation to increased revenues as described
above. Reimbursed expenses decreased primarily due to lower allocated personnel
costs.

            Operating income before income taxes, depreciation and amortization
(EBITDA) is a commonly used financial analysis tool for measuring and comparing
cable television companies in several areas, such as liquidity, operating
performance and leverage. EBITDA as a percentage of revenue increased from 41.2%
to 41.5% during the three months ended March 31, 1998 compared to the
corresponding period in 1997. The increase was primarily due to higher revenues
as described above. EBITDA increased from $373,600 to $383,200, or by 2.6%, for
the three months ended March 31, 1998 as compared to the corresponding period in
1997. EBITDA should be considered in addition to and not as a substitute for net
income and cash flows determined in accordance with generally accepted
accounting principles as an indicator of financial performance and liquidity.

            Depreciation and amortization expense decreased from $248,900 to
$209,600, or by 15.8%, for the three months ended March 31, 1998 as compared to
the corresponding period in 1997, due to the effect of certain intangible assets
becoming fully amortized.

            The Partnership's operating income increased from $124,700 to
$173,600, or by 39.2%, for the three months ended March 31, 1997 and 1998,
primarily due to decreases in depreciation and amortization expense and
increases in revenues as described above.

            Interest expense decreased from $61,200 to $60,600, or by 1.0%, for
the three months ended March 31, 1998 as compared to the corresponding period in
1997, due to lower average borrowings in the 1998 period.

            Due to the factors described above, the Partnership's net income
increased from $66,400 to $120,700, or by 81.8%, for the three months ended
March 31, 1998 as compared to the corresponding period in 1997.

LIQUIDITY AND CAPITAL RESOURCES

            The Partnership's primary objective, having invested its net
offering proceeds in cable systems, is to distribute to its partners all
available cash flow from operations and proceeds from the sale of cable systems,
if any, after providing for expenses, debt service and capital requirements
relating to the expansion, improvement and upgrade of its cable systems. The
Partnership's capital expenditures were $15,400 in the first quarter of 1998. As
of the date of this Report, 94% of the available channel capacity is being
utilized in the Partnership's systems that serve 78% of its customers. Beginning
in 1999, the Partnership intends to begin the upgrade of two systems, which
together serve 81% of the customers in this group of systems and




                                      -8-
<PAGE>   9

                    ENSTAR INCOME/GROWTH PROGRAM SIX-A, L.P.



LIQUIDITY AND CAPITAL RESOURCES (CONTINUED)

63% of the Partnership's total customer base. The upgrade program would increase
channel capacity in the Partnership's systems and is presently estimated to
require aggregate capital expenditures of approximately $4.2 million.

            On September 30, 1997, the Partnership entered into a loan agreement
with Enstar Finance Company, LLC ("EFC"), a subsidiary of the Corporate General
Partner, for a revolving loan facility of $4,563,000 (the "Facility") of which
$2,500,000 was advanced to the Partnership at closing. Such funds together with
available cash were used to repay the Partnership's previous note payable
balance of $2,525,000 and accrued interest expense. The Partnership's management
expects to increase borrowings under the Facility for the upgrade of the
Partnership's systems.

            The Partnership's Facility will mature on August 31, 2001, at which
time all funds previously advanced will be due in full. Borrowings bear interest
at the lender's base rate (8.5% at March 31, 1998) plus 0.625%, or at an
offshore rate plus 1.875%. The Partnership is permitted to prepay amounts
outstanding under the Facility at any time without penalty, and is able to
reborrow throughout the term of the Facility up to the maximum commitment then
available so long as no event of default exists. If the Partnership has excess
cash flow and its ratio of debt to cash flow exceeds 4.25 to 1, or it receives
proceeds from sales of its assets in excess of a specified amount, the
Partnership is required to make mandatory prepayments under the Facility. Such
prepayments permanently reduce the maximum commitment under the Facility.

            The Facility contains certain financial tests and other covenants
including, among others, restrictions on incurrence of indebtedness,
investments, sales of assets, acquisitions and other covenants, defaults and
conditions. The Partnership believes it was in compliance with the covenants at
March 31, 1998.

            The Corporate General Partner contributed its $269,300 receivable
balance from the Partnership for past due management fees and reimbursed
expenses as an equity contribution to EFC. As a result, this balance was not
paid on September 30, 1997 and remains an outstanding obligation of the
Partnership.

            The Facility does not restrict the payment of distributions to
partners unless an event of default exists thereunder or the ratio of debt to
cash flow is greater than 4 to 1. However, as a result of the pending upgrade
program discussed above, the Corporate General Partner has concluded that it is
not prudent for the Partnership to resume paying distributions at this time.

            Beginning in August 1997, the Partnership elected to self-insure its
cable distribution plant and subscriber connections against property damage as
well as possible business interruptions caused by such damage. The decision to
self-insure was made due to significant increases in the cost of insurance
coverage and decreases in the amount of insurance coverage available.

            While the Partnership has made the election to self-insure for these
risks based upon a comparison of historical damage sustained over the past five
years with the cost and amount of insurance currently available, there can be no
assurance that future self-insured losses will not exceed prior costs of
maintaining insurance for these risks. Approximately 73% of the Partnership's
subscribers are served by its system in Flora, Illinois and neighboring
communities. Significant damage to the system due to seasonal weather




                                      -9-

<PAGE>   10

                    ENSTAR INCOME/GROWTH PROGRAM SIX-A, L.P.



LIQUIDITY AND CAPITAL RESOURCES (CONTINUED)

conditions or other events could have a material adverse effect on the
Partnership's liquidity and cash flows. The Partnership continues to purchase
insurance coverage in amounts its management views as appropriate for all other
property, liability, automobile, workers' compensation and other types of
insurable risks.

            The "Year 2000" issue refers to certain contingencies that could
result from computer programs being written using two digits rather than four to
define the year. Many existing computer systems, including certain of the
Partnership's computer systems, process transactions based on two digits for the
year of the transaction (for example, "98" for 1998). These computer systems may
not operate effectively when the last two digits become "00," as will occur on
January 1, 2000.

            The Corporate General Partner has commenced an assessment of the
Partnership's Year 2000 business risks and its exposure to computer systems, to
operating equipment which is date sensitive and to the interface systems of its
vendors and service providers. Based on a preliminary study, the Corporate
General Partner has concluded that certain of the Partnership's information
systems were not Year 2000 compliant and has elected to replace such software
and hardware with Year 2000 compliant applications and equipment, although the
decision to replace major portions of such software and hardware had previously
been made without regard to the Year 2000 issue. The Corporate General Partner
expects to install substantially all of the new systems in 1998, with the
remaining systems to be installed in the first half of 1999. The total
anticipated cost, including replacement software and hardware, will be borne by
FHGLP.

            In addition to evaluating internal systems, the Corporate General
Partner has also initiated communications with third party vendors and service
suppliers to determine the extent to which the Partnership's interface systems
are vulnerable should those third parties fail to solve their own Year 2000
problems on a timely basis. There can be no assurance that the systems of other
companies on which the Partnership's systems rely will be timely converted and
that the failure to do so would not have an adverse impact on the Partnership's
systems. The Corporate General Partner continues to closely monitor Year 2000
developments with vendors and service suppliers.

            THREE MONTHS ENDED MARCH 31, 1998 AND 1997

            Cash provided by operating activities increased $8,900 in the three
months ended March 31, 1998 from the corresponding period in 1997. The
Partnership used $24,800 less cash to pay liabilities to third-party creditors
due to differences in the timing of payments. Changes in receivables and prepaid
expenses used $31,400 more cash in the first three months of 1998 than in the
corresponding period of 1997 due to differences in the timing of receivable
collections and in the payment of prepaid expenses.

            The Partnership used $12,100 less cash in investing activities
during the three months ended March 31, 1998 than in the comparable three months
of 1997, primarily due to decreases of $7,900 and $4,300 in expenditures for
tangible and intangible assets, respectively. Financing activities used $282,300
less cash in the first three months of 1998 than in the corresponding period in
1997, primarily due to a $300,000 scheduled debt payment made in the first
quarter of 1997. The Partnership used $17,100 more cash for the payment of
amounts owed to the Corporate General Partner due to differences in the timing
of payments.




                                      -10-

<PAGE>   11

                    ENSTAR INCOME/GROWTH PROGRAM SIX-A, L.P.

INFLATION

            Certain of the Partnership's expenses, such as those for wages and
benefits, equipment repair and replacement, and billing and marketing generally
increase with inflation. However, the Partnership does not believe that its
financial results have been, or will be, adversely affected by inflation in a
material way, provided that it is able to increase its service rates
periodically, of which there can be no assurance.







                                      -11-

<PAGE>   12

                    ENSTAR INCOME/GROWTH PROGRAM SIX-A, L.P.




PART II.          OTHER INFORMATION


ITEMS 1-5.        Not applicable.

ITEM 6.           Exhibits and Reports on Form 8-K

                  (a)      None.

                  (b)      No reports on Form 8-K were filed during the quarter
                           for which this report is filed.



<PAGE>   13

                                   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.





                    ENSTAR INCOME/GROWTH PROGRAM SIX-A, L.P.

                          a GEORGIA LIMITED PARTNERSHIP
                          -----------------------------
                                  (Registrant)



                                      By: ENSTAR COMMUNICATIONS CORPORATION
                                          General Partner






Date:  May 14, 1998                   By: /s/ Michael K. Menerey
                                          --------------------------------
                                          Michael K. Menerey,
                                          Executive Vice President,
                                          Chief Financial Officer and
                                          Secretary