<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   0-13333
                                              -----------
Enstar Income Program 1984-1, L.P.
--------------------------------------------------------------------------------
             (Exact name of Registrant as specified in its charter)

            Georgia                                        58-1581136
----------------------------------               ------------------------------
(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 PROGRAM 1984-1, L.P.

                            CONDENSED BALANCE SHEETS

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

<TABLE>
<CAPTION>
                                                  December 31,       March 31,
                                                     1996*             1997
                                                 -------------    -------------
                                                                   (Unaudited)
<S>                                              <C>              <C>          
ASSETS:
   Cash and cash equivalents                     $   1,004,400    $     903,600

   Receivables, less allowance of $35,100 and
      $47,700 for possible losses                      187,100          185,600

   Prepaid expenses and other assets                   129,600          151,800

   Property, plant and equipment, less accumulated
      depreciation and amortization of $10,104,300
      and $10,220,300                                3,158,800        3,152,100

   Franchise cost, net of accumulated
      amortization of $214,300 and $219,500             76,800           72,400

   Deferred loan costs and other charges, net           48,500           52,400
                                                 -------------    -------------
                                                 $   4,605,200    $   4,517,900
                                                 =============    =============

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

LIABILITIES:
   Accounts payable                              $     448,700    $     368,500
   Due to affiliates                                 1,393,800        1,502,700
   Note payable                                      1,042,800          542,800
                                                 -------------    -------------
            TOTAL LIABILITIES                        2,885,300        2,414,000
                                                 -------------    -------------

COMMITMENTS AND CONTINGENCIES

PARTNERSHIP CAPITAL (DEFICIT):
   General partners                                    (55,500)         (51,700)
   Limited partners                                  1,775,400        2,155,600
                                                 -------------    -------------

            TOTAL PARTNERSHIP CAPITAL                1,719,900        2,103,900
                                                 -------------    -------------
                                                 $   4,605,200    $   4,517,900
                                                 =============    =============
</TABLE>

               *As presented in the audited financial statements.

            See accompanying notes to condensed financial statements.


                                       2

<PAGE>   3

                       ENSTAR INCOME PROGRAM 1984-1, L.P.

                       CONDENSED STATEMENTS OF OPERATIONS

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


<TABLE>
<CAPTION>
                                                             Unaudited
                                                   ----------------------------
                                                         Three months ended
                                                             March 31,
                                                   ----------------------------
                                                       1996             1997
                                                   -----------      -----------
<S>                                                <C>              <C>        
REVENUES                                           $ 1,263,500      $ 1,368,900
                                                   -----------      -----------

OPERATING EXPENSES:
   Service costs                                       464,400          495,200
   General and administrative expenses                 165,400          197,300
   General Partner management fees
      and reimbursed expenses                          129,800          138,500
   Depreciation and amortization                       166,700          136,500
                                                   -----------      -----------
                                                       926,300          967,500
                                                   -----------      -----------
OPERATING INCOME                                       337,200          401,400
                                                   -----------      -----------
OTHER INCOME (EXPENSE):
   Interest income                                      10,500           11,600
   Interest expense                                    (52,000)         (29,000)
                                                   -----------      -----------
                                                       (41,500)         (17,400)
                                                   -----------      -----------
NET INCOME                                         $   295,700      $   384,000
                                                   ===========      ===========
NET INCOME PER UNIT OF LIMITED
   PARTNERSHIP INTEREST                            $      9.78      $     12.70
                                                   ===========      ===========
AVERAGE LIMITED PARTNERSHIP
   UNITS OUTSTANDING DURING PERIOD                      29,940           29,940
                                                   ===========      ===========
</TABLE>

            See accompanying notes to condensed financial statements.


                                       3

<PAGE>   4

                       ENSTAR INCOME PROGRAM 1984-1, 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                                              $   295,700    $   384,000
   Adjustments to reconcile net income to net cash
      provided by operating activities:
        Depreciation and amortization                          166,700        136,500
        Amortization of deferred loan costs                      1,000          6,100
        Increase (decrease) from changes in:
           Accounts receivable, prepaid expenses
              and other assets                                  10,700        (20,700)
           Accounts payable and due to affiliates              161,600         28,700
                                                           -----------    -----------

               Net cash provided by operating activities       635,700        534,600
                                                           -----------    -----------

CASH FLOWS FROM INVESTING ACTIVITIES:
   Capital expenditures                                        (63,000)      (122,600)
   Increase in intangible assets                               (11,500)       (12,800)
                                                           -----------    -----------

               Net cash used in investing activities           (74,500)      (135,400)
                                                           -----------    -----------

CASH FLOWS FROM INVESTING ACTIVITIES:
   Repayment of debt                                             --          (500,000)
                                                           -----------    -----------

INCREASE (DECREASE) IN CASH AND CASH
   EQUIVALENTS                                                 561,200       (100,800)

CASH AND CASH EQUIVALENTS
   AT BEGINNING OF PERIOD                                      935,300      1,004,400
                                                           -----------    -----------

CASH AND CASH EQUIVALENTS
   AT END OF PERIOD                                        $ 1,496,500    $   903,600
                                                           ===========    ===========
</TABLE>

           See accompanying notes to condensed financial statements.


                                       4

<PAGE>   5

                       ENSTAR INCOME PROGRAM 1984-1, 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 $68,400
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 $70,100 for
the three months ended March 31, 1997. Management fees and reimbursed expenses
due the General Partner are non-interest bearing.

           Payments of management fees and reimbursed expenses were deferred in
1994, 1995 and 1996 pursuant to restrictions in the note payable agreement. See
Item 2., Management's Discussion and Analysis of Financial Condition and Results
of Operations - Liquidity and Capital Resources. The cumulative amount deferred
as of March 31, 1997 was approximately $1,081,300. The Partnership will be
obligated to pay these deferred management fees and reimbursed expenses at the
point in time the restrictions imposed by the note payable agreement are
removed. Effective March 27, 1996, the restrictions in the note payable were
changed to permit the current payment of management fees and reimbursed
expenses; however, the Partnership continues to be prohibited from paying any
previously deferred fees.

           The Partnership also receives certain system operating management
services from affiliates of the General Partner in addition to the Manager due
to the fact that there are no such employees directly employed by the
Partnership. The Partnership reimburses the affiliates for its allocable share
of the affiliates' operational costs. The total amount charged to the
Partnership for these costs approximated $27,300 in the three months ended March
31, 1997. No management fee is payable to the affiliates by the Partnership and
there is no duplication of reimbursed expenses and costs paid to the Manager.



                                       5

<PAGE>   6

                       ENSTAR INCOME PROGRAM 1984-1, L.P.

                     NOTES TO CONDENSED FINANCIAL STATEMENTS
                                   (CONCLUDED)

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

2.         TRANSACTIONS WITH THE GENERAL PARTNER AND AFFILIATES (CONCLUDED)

           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 General Partner could negotiate for such
programming services for the 15 partnerships managed by the General Partner as a
group. The Partnership recorded programming fee expense of $303,500 for the
three months ended March 31, 1997. Programming fees are included in service
costs in the statements of operations.

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.

5.         SUBSEQUENT EVENT

           On May 2, 1997, the Partnership prepaid the remaining $292,800
balance of its note payable and the related accrued interest.



                                       6

<PAGE>   7

                       ENSTAR INCOME PROGRAM 1984-1, 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 $1,263,500 to $1,368,900,
or by 8.3%, for the quarter ended March 31, 1997 as compared to the
corresponding period in 1996. Of the $105,400 increase, $114,800 was due to
increases in regulated service rates that were implemented by the Partnership in
the second and fourth quarters of 1996, $34,900 was due to the restructuring of
The Disney Channel from a premium channel to a tier channel effective July 1,
1996 and $3,300 was due to increases in other revenue producing items. These
increases were partially offset by a decrease of $47,600 due to decreases in the
number of subscriptions for basic, premium and tier services. As of March 31,
1997, the Partnership had approximately 11,800 homes subscribing to cable
service and 5,800 premium service units.

           Service costs increased from $464,400 to $495,200, or by 6.6%, 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 $30,800 increase, $19,600 was related to increased
programming fees charged by program suppliers (including primary satellite
fees), $18,900 was due to an increase in copyright fees and $16,800 was due to
an increase in franchise fees. These increases were partially offset by a
$19,200 decrease in personnel costs and a $7,900 increase in capitalization of
labor and overhead expense due to a greater number of capital projects during
the 1997 quarter. The increase in programming fees included a



                                       7

<PAGE>   8
                       ENSTAR INCOME PROGRAM 1984-1, L.P.


RESULTS OF OPERATIONS (CONCLUDED)

$10,000 increase related to the restructuring of The Disney Channel discussed
above. Increases in copyright fees and franchise fees resulted from increased
revenues as described above. The franchise fee increase also included a $12,000
increase due to a non-recurring charge in the first quarter of 1997 related to
1996 franchise fee payments made during the quarter which exceeded estimates
recorded as of December 31, 1996.

           General and administrative expenses increased from $165,400 to
$197,300, or by 19.3%, for the quarter ended March 31, 1997 as compared to the
corresponding period in 1996. Of the $31,900 increase, $25,700 was due to an
increase in bad debt expense and $9,900 was due to higher insurance premiums.
These decreases were partially offset by a $9,000 decrease in business tax
expense. The remaining $5,300 increase was composed of nominal increases in
various other accounts.

           Management fees and reimbursed expenses increased from $129,800 to
$138,500, or by 6.7%, for the quarter ended March 31, 1997 as compared to the
corresponding period in 1996. Management fees increased by $5,200 in direct
relation to increased revenues as described above. Reimbursable expenses
increased by $3,500, primarily due to higher allocated personnel costs,
professional fees and telephone expense.

           Depreciation and amortization expense decreased from $166,700 to
$136,500, or by 18.1%, for the quarter ended March 31, 1997 as compared to the
corresponding period in 1996, due to the effect of certain plant assets becoming
fully depreciated.

           Operating income increased from $337,200 to $401,400, or by 19.0%,
for the quarter ended March 31, 1996 as compared to the corresponding period in
1996, primarily due to increases in revenues and decreases in depreciation and
amortization expense as described above.

           Interest expense decreased from $52,000 to $29,000, or by 44.2%, for
the quarter ended March 31, 1997 as compared to the corresponding period in
1996, primarily due to a decrease in average borrowings from $1,942,800 in the
first three months of 1996 to $903,900 in the comparable 1997 quarter.

           Interest income increased from $10,500 to $11,600, or by 10.5%, for
the quarter ended March 31, 1997 as compared to the corresponding period in
1996, primarily due to a change in investment policy that yielded a higher
return on invested cash. The increase was partially offset by a decrease in the
average investment balance due to a $500,000 prepayment of outstanding
borrowings during the first three months of 1997.

           Due to the factors described above, the Partnership's net income
increased from $295,700 to $384,000 for the quarter ended March 31, 1997 as
compared to 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


                                       8

<PAGE>   9
                       ENSTAR INCOME PROGRAM 1984-1, L.P.


LIQUIDITY AND CAPITAL RESOURCES (CONTINUED)

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
and are projected to be approximately $715,000 for 1997. As of the date of this
Report, substantially all of the available channel capacity in the Partnership's
systems is being utilized and each of such systems requires rebuilding. The
rebuild program is presently estimated to require aggregate capital expenditures
of approximately $7.5 million, although the majority of the total is not planned
to be spent until 1998. Due to the fact that the Partnership is currently not
able to incur additional borrowings, there can be no assurance that the
Partnership's cash flow will be adequate to meet its liquidity requirements,
including necessary capital expenditures. As a result, the Partnership may seek
additional sources of borrowed funds in the future, if such borrowings are
available on terms acceptable to the Partnership, of which there can be no
assurance.

           On March 7, 1997, the Partnership prepaid $500,000 of its note
payable balance. On April 9, 1997, the Partnership made a scheduled principal
repayment of $250,000 on the note payable, and on May 2, 1997, the Partnership
prepaid the remaining balance of $292,800 and the related accrued interest. On
March 27, 1996, the note payable, which until that date had restricted the
payment of management fees and reimbursed expenses to the Manager, was amended
to permit the current payment of management fees and reimbursed expenses (but
not deferred management fees and reimbursed expenses). As of March 31, 1997,
deferred management fees and reimbursed expenses totaled an aggregate of
$1,081,300. In order to preserve liquidity, the Partnership does not currently
intend to pay the deferred management fees and reimbursed expenses, but will
periodically re-evaluate this position.

           The General Partner may seek a buyer for the Snow Hill, North
Carolina system as well as for the Kershaw, South Carolina system. The sale of
these systems would allow the Partnership to accelerate the rebuilding of its
remaining systems. Upon the sale of either or both of these systems, the General
Partner would evaluate the feasibility at that time of resuming the payment of
distributions. Due to current cable television system market conditions, there
is currently no activity being conducted by the General Partner with respect to
selling these systems, and there can, therefore, be no assurance that these
systems can be sold at an acceptable price.

           THREE MONTHS ENDED MARCH 31, 1997 AND 1996

           Operating activities provided $101,100 less cash in the three months
ended March 31, 1997 than in the corresponding period in 1996. The Partnership
used $132,900 more cash to pay liabilities owed to affiliates and third-party
creditors resulting from differences in the timing of payments. Changes in
accounts receivable, prepaid expenses and other assets used $31,400 more cash in
the first three months of 1997 due to differences in the timing of receivable
collections and in the payment of prepaid expenses. Cash generated by
Partnership operations increased by $63,200 after adding back non-cash
depreciation and amortization charges.



                                       9

<PAGE>   10
                       ENSTAR INCOME PROGRAM 1984-1, L.P.


LIQUIDITY AND CAPITAL RESOURCES (CONCLUDED)

           The Partnership used $60,900 more cash in investing activities in the
three months ended March 31, 1997 than in the corresponding three months of
1996, due to a $59,600 increase in expenditures for tangible assets and a $1,300
increase in expenditures for intangible assets. Financing activities used
$500,000 more cash in the first three months of 1997 for the repayment of debt
discussed above.

           Operating income before depreciation and amortization (EBITDA) as a
percentage of revenues decreased from 39.9% during the first three months of
1996 to 39.3% in the corresponding 1997 quarter. The decrease was primarily due
to higher bad debt expense, programming fees, copyright fees and franchise fees.
EBITDA increased from $503,900 to $537,900, or by 6.7%, during the quarter ended
March 31, 1997 compared to the corresponding three months in 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 PROGRAM 1984-1, 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 PROGRAM 1984-1, L.P.
                          a GEORGIA LIMITED PARTNERSHIP
                       ----------------------------------
                                  (Registrant)



                                       By:     ENSTAR COMMUNICATIONS CORPORATION
                                               General Partner



Date:  May 12, 1997                    By:     /s/ Michael K. Menerey
                                               ---------------------------------
                                               Michael K. Menerey,
                                               Chief Financial Officer