<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, 1997
                               ----------------------

                                       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,
                                                                         1996*             1997
                                                                      ------------      -----------
                                                                                        (Unaudited)
<S>                                                                   <C>               <C>        
ASSETS:
   Cash and cash equivalents                                          $   169,400       $    46,800

   Accounts receivable, less allowance of $5,100 and
      $5,600 for possible losses                                          116,100           120,300

   Prepaid expenses and other                                              36,800            38,700

   Property, plant and equipment, less accumulated
      depreciation and amortization of $4,369,400 and $4,496,100        3,881,100         3,760,600

   Franchise cost, net of accumulated
      amortization of $3,505,100 and $3,607,600                         1,421,100         1,324,000

   Deferred loan costs and other, net                                      32,700            31,500
                                                                      -----------       -----------

                                                                      $ 5,657,200       $ 5,321,900
                                                                      ===========       ===========

                                  LIABILITIES AND PARTNERSHIP CAPITAL
                                  -----------------------------------
LIABILITIES:
   Accounts payable                                                   $   454,500       $   346,400
   Due to affiliates                                                      441,500           447,900
   Note payable                                                         3,125,000         2,825,000
                                                                      -----------       -----------

            TOTAL LIABILITIES                                           4,021,000         3,619,300
                                                                      -----------       -----------

COMMITMENTS AND CONTINGENCIES

PARTNERSHIP CAPITAL (DEFICIT):
   General partners                                                      (146,300)         (145,600)
   Limited partners                                                     1,782,500         1,848,200
                                                                      -----------       -----------

            TOTAL PARTNERSHIP CAPITAL                                   1,636,200         1,702,600
                                                                      -----------       -----------

                                                                      $ 5,657,200       $ 5,321,900
                                                                      ===========       ===========
</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,
                                                    ---------------------------
                                                       1996              1997
                                                    ---------         ---------
<S>                                                 <C>               <C>      
REVENUES                                            $ 851,300         $ 905,800
                                                    ---------         ---------

OPERATING EXPENSES:
   Service costs                                      276,800           299,000
   General and administrative expenses                108,900           102,000
   General Partner management fees
      and reimbursed expenses                         112,100           131,200
   Depreciation and amortization                      403,700           248,900
                                                    ---------         ---------

                                                      901,500           781,100
                                                    ---------         ---------

OPERATING INCOME (LOSS)                               (50,200)          124,700
                                                    ---------         ---------

OTHER INCOME (EXPENSE):
   Interest income                                      3,400             2,800
   Interest expense                                   (81,800)          (61,200)
   Gain on sale of cable assets                          --                 100
                                                    ---------         ---------

                                                      (78,400)          (58,300)
                                                    ---------         ---------

NET INCOME (LOSS)                                   $(128,600)        $  66,400
                                                    =========         =========

NET INCOME (LOSS) PER UNIT OF LIMITED
   PARTNERSHIP INTEREST                             $   (1.60)        $     .82
                                                    =========         =========

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,
                                                                        -------------------------
                                                                           1996            1997
                                                                        ---------       ---------
<S>                                                                     <C>             <C>      
CASH FLOWS FROM OPERATING ACTIVITIES:
   Net income (loss)                                                    $(128,600)      $  66,400
   Adjustments to reconcile net income (loss) to net cash
      provided by operating activities:
        Depreciation and amortization                                     403,700         248,900
        Amortization of deferred loan costs                                 5,700           3,800
        Gain on sale of cable assets                                         --              (100)
        Increase (decrease) from changes in:
           Accounts receivable, prepaid expenses and other assets          10,900          (6,100)
           Accounts payable                                               (65,300)       (108,100)
                                                                        ---------       ---------

               Net cash provided by operating activities                  226,400         204,800
                                                                        ---------       ---------

CASH FLOWS FROM INVESTING ACTIVITIES:
   Capital expenditures                                                   (16,900)        (23,300)
   Increase in intangible assets                                           (9,700)        (10,300)
   Proceeds from sale of property, plant and equipment                       --               100
                                                                        ---------       ---------

               Net cash used in investing activities                      (26,600)        (33,500)
                                                                        ---------       ---------

CASH FLOWS FROM FINANCING ACTIVITIES:
   Deferred loan costs                                                     (3,700)           (300)
   Repayment of debt                                                         --          (300,000)
   Due to affiliates                                                      127,500           6,400
                                                                        ---------       ---------

               Net cash provided by (used in) financing activities        123,800        (293,900)
                                                                        ---------       ---------

INCREASE (DECREASE) IN CASH AND CASH
   EQUIVALENTS                                                            323,600        (122,600)

CASH AND CASH EQUIVALENTS
   AT BEGINNING OF PERIOD                                                 175,800         169,400
                                                                        ---------       ---------

CASH AND CASH EQUIVALENTS
   AT END OF PERIOD                                                     $ 499,400       $  46,800
                                                                        =========       =========
</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, 1997 and 1996 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, 1997 are not necessarily indicative of results
for the entire year.

2.         TRANSACTIONS WITH THE GENERAL PARTNER 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 $45,300
for the three months ended March 31, 1997.

           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. 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 $85,900 for
the three months ended March 31, 1997. 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 $11,600 for the three
months ended March 31, 1997. 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
$194,000 for the three months ended March 31, 1997. 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
                                   (CONCLUDED)
                     =======================================


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 are allocated 99% to the limited partners and
1% to the general partners.

4.         RECLASSIFICATIONS

           Certain 1996 amounts have been reclassified to conform to the 1997
presentation.





                                      -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

           On February 8, 1996, President Clinton signed into law the
Telecommunications Act of 1996 (the "1996 Telecom Act"). This statute
substantially changed the competitive and regulatory environment for
telecommunications providers by significantly amending the Communications Act of
1934, including certain of the rate regulation provisions previously imposed by
the Cable Television Consumer Protection and Competition Act of 1992 (the "1992
Cable Act"). Compliance with those rate regulations has had a negative impact on
the Partnership's revenues and cash flow. The 1996 Telecom Act provides that
certain of the rate regulations will be phased out altogether in 1999. Further,
the regulatory environment will continue to change pending, among other things,
the outcome of legal challenges and FCC rulemaking and enforcement activity in
respect of the 1992 Cable Act and the 1996 Telecom Act. 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, 1996 for additional information regarding
such matters and the effect thereof on the Partnership's business.

RESULTS OF OPERATIONS

           The Partnership's revenues increased from $851,300 to $905,800, or by
6.4%, for the quarter ended March 31, 1997 as compared to the corresponding
period in 1996. Of the $54,500 increase, $56,100 was due to increases in
regulated service rates that were implemented by the Partnership in the second
and fourth quarters of 1996, $18,600 was due to the restructuring of The Disney
Channel from a premium channel to a tier channel effective July 1, 1996 and
$7,900 was due to an increase in advertising sales revenue. These increases were
partially offset by a $20,500 decrease due to decreases in the number of
subscriptions for basic and premium services and a $7,600 decrease in other
revenue producing items. As of March 31, 1997, the Partnership had approximately
9,700 homes subscribing to cable service and 2,700 premium service units.

           Service costs increased from $276,800 to $299,000, or by 8.0%, for
the quarter ended March 31, 1997 as compared to the corresponding period in
1996. Service costs represent costs directly attributable to providing cable
services to customers. Of the $22,200 increase, $17,800 was due to increases in
programming fees (including primary satellite fees) and $5,300 was due to an
increase in copyright fees. The increase in programming fees included a $5,200
increase related to the restructuring of The Disney Channel discussed above.




                                      -7-
<PAGE>   8
                    ENSTAR INCOME/GROWTH PROGRAM SIX-A, L.P.


RESULTS OF OPERATIONS (CONCLUDED)

           General and administrative expenses decreased from $108,900 to
$102,000, or by 6.3%, for the quarter ended March 31, 1997 as compared to the
corresponding period in 1996. Of the $6,900 decrease, $5,300 was due to lower
insurance premiums and $1,600 was due to nominal decreases in various other
accounts.

           Management fees and reimbursed expenses increased from $112,100 to
$131,200, or by 17.0%, for the quarter ended March 31, 1997 as compared to the
corresponding period in 1996. Of the $19,100 increase, reimbursed expenses
increased by $16,400, primarily due to higher allocated personnel costs
resulting from staff additions and wage increases. Management fees increased by
$2,700 in direct relation to increased revenues as described above.

           Depreciation and amortization expense decreased from $403,700 to
$248,900, or by 38.3%, for the quarter ended March 31, 1997 as compared to the
corresponding period in 1996, due to the effect of certain intangible assets
becoming fully amortized.

           The Partnership generated operating income of $124,700 for the
quarter ended March 31, 1997 compared to an operating loss of $50,200 for the
corresponding period in 1996 primarily due to decreases in depreciation and
amortization expense and increases in revenues as described above.

           Interest expense decreased from $81,800 to $61,200, or by 25.2%, for
the quarter ended March 31, 1997 as compared to the corresponding period in
1996, due to lower average interest rates (8.8% in the 1996 quarter versus 6.9%
for the first three months of 1997) and a decrease in average borrowings from
$4,125,000 in the first quarter of 1996 to $3,125,000 for the quarter ended
March 31, 1997.

           Due to the factors described above, the Partnership generated net
income of $66,400 for the quarter ended March 31, 1997 compared to a net loss of
$128,600 for the corresponding period in 1996.

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
currently relies exclusively on the availability of cash generated from
operations to fund its ongoing expenses, debt service and capital requirements.
In general, these requirements involve expansion, improvement and upgrade of the
Partnership's existing cable systems. The Partnership's capital expenditures are
projected to be $250,000 for 1997. As of the date of this Report, 95% of the
available channel capacity is being utilized in the Partnership's systems that
serve 74% of its customers. In 1998, the Partnership intends to begin the
rebuild of two systems, which together serve 86% of the customers in this group
of systems and 64% of the Partnership's total customer base. The rebuild program
is presently estimated to require aggregate capital expenditures of
approximately $3.0 million. Funding rebuild capital expenditures will require
refinancing the Partnership's term loan agreement and there can be no assurance
that the Partnership will be able to obtain such a refinancing on terms
acceptable to the Partnership.




                                      -8-
<PAGE>   9
                    ENSTAR INCOME/GROWTH PROGRAM SIX-A, L.P.


LIQUIDITY AND CAPITAL RESOURCES (CONTINUED)

           The Partnership has $2,825,000 outstanding under its term loan
agreement. On December 18, 1996, the Partnership amended its term loan agreement
(the "Amendment") to, among other things, extend the maturity date by 12 months
from December 31, 1996 to December 31, 1997. The Amendment increases the
quarterly principal payments from $250,000 in 1996 to $300,000 through September
30, 1997. The remaining balance of $2,225,000 is due on December 31, 1997. The
Partnership paid a fee of $15,000 for the Amendment. To fund its debt service
payments, the Partnership will be required to defer the payment of a portion of
its 1997 management fees and reimbursable expenses due the Corporate General
Partner. Additionally, the Partnership will defer the payment of certain
programming fees due an affiliate. As of March 31, 1997, the Partnership owed
the Corporate General Partner $223,000 for management fees and reimbursable
expenses, and also owed an affiliate in excess of $78,500 for programming fees.

           Management's 1997 cash flow projections indicate that operating cash
flows will not be sufficient to fund the required final debt payment due on
December 31, 1997. Management is in the process of evaluating certain strategies
to meet this obligation, which include refinancing the indebtedness. The
Partnership has been successful in negotiating extensions of the maturity date
over the past three years and expects to do so again in 1997, if required.
However, there can be no assurance that the Partnership will be successful in
negotiating a new debt agreement or extension of the current agreement, and, if
successful, on terms favorable to the Partnership.

           The amended term loan agreement restricts the Partnership from paying
distributions to the partners during the term of the agreement. The term loan
agreement also contains certain financial tests and other covenants including,
among others, restrictions on incurrence of indebtedness, investments, sale of
assets, acquisitions, and other covenants, defaults and conditions. Management
believes the Partnership was in compliance with its debt covenants as of March
31, 1997.

           THREE MONTHS ENDED MARCH 31, 1997 AND 1996

           Cash provided by operating activities decreased by $21,600 in the
three months ended March 31, 1997 from the corresponding period of the prior
year. The Partnership used $42,800 more cash to pay amounts owed to third party
creditors in the first quarter of 1997 than in the comparable period of 1996 due
to differences in the timing of payments. Changes in receivables and prepaid
expenses provided $17,000 less cash in the first three months of 1997 as
compared to the first three months of 1996 due to differences in the timing of
receivable collections and in the payment of prepaid expenses. Cash generated by
Partnership operations increased by $38,200 in the first quarter of 1997 after
adding back non-cash depreciation and amortization charges.

           The Partnership used $6,900 more cash in investing activities during
the three months ended March 31, 1997 than in the comparable three months of
1996 primarily due to increases of $6,400 in expenditures for tangible assets
and $600 in expenditures for intangible assets. Financing activities used
$417,700 more cash in the quarter ended March 31, 1997 principally due to a
$300,000 scheduled debt repayment. Changes in amounts owed to affiliates
provided $121,100 less cash in the first three months of 1997. In the comparable
quarter of 1996, the Partnership deferred payment of a greater portion of the
management fees and reimbursed expenses due the Corporate General Partner than
in the 1997 period. The Partnership used




                                      -9-
<PAGE>   10
                    ENSTAR INCOME/GROWTH PROGRAM SIX-A, L.P.


LIQUIDITY AND CAPITAL RESOURCES (CONCLUDED)

$3,400 less cash for the payment of deferred loan costs related to the
Partnership's loan agreement in the first three months of 1997.

           Operating income before depreciation and amortization (EBITDA) as a
percentage of revenue decreased from 41.5% during the first three months of 1996
to 41.2% during the corresponding 1997 period. The decrease was primarily due to
higher programming fees. EBITDA increased from $353,500 to $373,600, or by 5.7%,
for the three months ended March 31, 1997 compared to the first three months of
1996.

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.




                                      -10-
<PAGE>   11
                    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>   12
                                   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 6, 1997                    By:  /s/ Michael K. Menerey
                                          ----------------------------
                                          Michael K. Menerey,
                                          Chief Financial Officer