<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    June 30, 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   0-13333
                                                 ---------

                       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 
                                             -----   -----


                        Exhibit Index located at Page E-1

<PAGE>   2
                         PART I - FINANCIAL INFORMATION

                       ENSTAR INCOME PROGRAM 1984-1, L.P.

                            CONDENSED BALANCE SHEETS

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


<TABLE>
<CAPTION>
                                                                          December 31,         June 30,
                                                                              1997*              1998
                                                                          -----------         -----------
                                                                                              (Unaudited)
<S>                                                                       <C>                 <C>        
ASSETS:
   Cash and cash equivalents                                              $   462,900         $   625,400

   Accounts receivable, less allowance of $28,000 and
      $7,400 for possible losses                                              107,500              79,800

   Insurance claim receivable                                                 399,700             392,400

   Prepaid expenses and other assets                                          135,800             160,700

   Property, plant and equipment, less accumulated
      depreciation and amortization of $10,477,900 and $10,765,000          3,387,200           3,522,000

   Franchise cost, net of accumulated
      amortization of $235,400 and $108,200                                    74,600              67,300

   Deferred loan costs and other charges, net                                 128,400             110,300
                                                                          -----------         -----------

                                                                          $ 4,696,100         $ 4,957,900
                                                                          ===========         ===========

                       LIABILITIES AND PARTNERSHIP CAPITAL
                       -----------------------------------
LIABILITIES:
   Accounts payable                                                       $   529,800         $   442,100
   Due to affiliates                                                          754,200             752,800
   Note payable - affiliate                                                   250,000               --
                                                                          -----------         -----------

          TOTAL LIABILITIES                                                 1,534,000           1,194,900
                                                                          -----------         -----------

COMMITMENTS AND CONTINGENCIES

PARTNERSHIP CAPITAL (DEFICIT):
   General partner                                                            (41,100)            (35,100)
   Limited partners                                                         3,203,200           3,798,100
                                                                          -----------         -----------

          TOTAL PARTNERSHIP CAPITAL                                         3,162,100           3,763,000
                                                                          -----------         -----------

                                                                          $ 4,696,100         $ 4,957,900
                                                                          ===========         ===========
</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
                                                                 June 30,
                                                      -------------------------------
                                                         1997                 1998
                                                      -----------         -----------
<S>                                                   <C>                 <C>        
REVENUES                                              $ 1,331,700         $ 1,317,300
                                                      -----------         -----------
                                                
OPERATING EXPENSES:                             
   Service costs                                          484,200             466,500
   General and administrative expenses                    265,200             177,400
   General Partner management fees              
      and reimbursed expenses                             142,300             169,500
   Depreciation and amortization                          139,800             182,400
                                                      -----------         -----------
                                                
                                                        1,031,500             995,800
                                                      -----------         -----------
                                                
OPERATING INCOME                                          300,200             321,500
                                                      -----------         -----------
                                                
OTHER INCOME (EXPENSE):                         
   Interest income                                          7,500               7,300
   Interest expense                                       (45,900)            (28,000)
                                                      -----------         -----------
                                                
                                                          (38,400)            (20,700)
                                                      -----------         -----------
                                                
NET INCOME                                            $   261,800         $   300,800
                                                      ===========         ===========
                                                
Net income allocated to General Partner               $     2,600         $     3,000
                                                      ===========         ===========
                                                
Net income allocated to Limited Partners              $   259,200         $   297,800
                                                      ===========         ===========
                                                
NET INCOME PER UNIT OF LIMITED                  
   PARTNERSHIP INTEREST                               $      8.66         $      9.95
                                                      ===========         ===========
                                                
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.

                       CONDENSED STATEMENTS OF OPERATIONS

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


<TABLE>
<CAPTION>
                                                         Unaudited
                                                -------------------------------
                                                       Six months ended
                                                          June 30,
                                                -------------------------------
                                                   1997                 1998
                                                -----------         -----------
<S>                                             <C>                 <C>        
REVENUES                                        $ 2,700,600         $ 2,647,300
                                                -----------         -----------

OPERATING EXPENSES:
   Service costs                                    979,400             946,500
   General and administrative expenses              462,500             358,300
   General Partner management fees
      and reimbursed expenses                       280,800             337,000
   Depreciation and amortization                    276,300             360,800
                                                -----------         -----------

                                                  1,999,000           2,002,600
                                                -----------         -----------

OPERATING INCOME                                    701,600             644,700
                                                -----------         -----------

OTHER INCOME (EXPENSE):
   Interest income                                   19,100              11,800
   Interest expense                                 (74,900)            (55,600)
                                                -----------         -----------

                                                    (55,800)            (43,800)
                                                -----------         -----------

NET INCOME                                      $   645,800         $   600,900
                                                ===========         ===========

Net income allocated to General Partner         $     6,500         $     6,000
                                                ===========         ===========

Net income allocated to Limited Partners        $   639,300         $   594,900
                                                ===========         ===========

NET INCOME PER UNIT OF LIMITED
   PARTNERSHIP INTEREST                         $     21.35         $     19.87
                                                ===========         ===========

AVERAGE LIMITED PARTNERSHIP
   UNITS OUTSTANDING DURING PERIOD                   29,940              29,940
                                                ===========         ===========
</TABLE>


           See accompanying notes to condensed financial statements.



                                      -4-
<PAGE>   5

                       ENSTAR INCOME PROGRAM 1984-1, L.P.

                            STATEMENTS OF CASH FLOWS

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


<TABLE>
<CAPTION>
                                                                          Unaudited
                                                               -------------------------------
                                                                       Six months ended
                                                                           June 30,
                                                               -------------------------------
                                                                   1997               1998
                                                               -----------         -----------
<S>                                                            <C>                 <C>        
CASH FLOWS FROM OPERATING ACTIVITIES:
   Net income                                                  $   645,800         $   600,900
   Adjustments to reconcile net income to net cash
      provided by operating activities:
       Depreciation and amortization                               276,300             360,800
       Amortization of deferred loan costs                          44,500              14,600
       Increase (decrease) from changes in:
         Receivables, prepaid expenses and other assets             (6,900)             10,100
         Accounts payable                                           82,000             (87,700)
                                                               -----------         -----------

             Net cash provided by operating activities           1,041,700             898,700
                                                               -----------         -----------

CASH FLOWS FROM INVESTING ACTIVITIES:
   Capital expenditures                                           (295,900)           (478,600)
   Increase in intangible assets                                   (24,900)             (2,200)
                                                               -----------         -----------

             Net cash used in investing activities                (320,800)           (480,800)
                                                               -----------         -----------

CASH FLOWS FROM FINANCING ACTIVITIES:
   Due to affiliates                                                88,000              (1,400)
   Repayment of debt                                            (1,042,800)           (250,000)
   Deferred loan costs                                              --                  (4,000)
                                                               -----------         -----------

             Net cash used in financing activities                (954,800)           (255,400)
                                                               -----------         -----------

INCREASE (DECREASE) IN CASH AND
   CASH EQUIVALENTS                                               (233,900)            162,500

CASH AND CASH EQUIVALENTS
   AT BEGINNING OF PERIOD                                        1,004,400             462,900
                                                               -----------         -----------

CASH AND CASH EQUIVALENTS
   AT END OF PERIOD                                            $   770,500         $   625,400
                                                               ===========         ===========
</TABLE>


           See accompanying notes to condensed financial statements.



                                      -5-
<PAGE>   6
                       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
and six months ended June 30, 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 and six months ended June 30, 1998 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 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 $65,900 and $132,400
for the three and six months ended June 30, 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 General Partner and its subsidiary are charged a
proportionate share of these expenses. The 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 $103,600 and
$204,600 for the three and six months ended June 30, 1998. Management fees and
reimbursed expenses due the General Partner are non-interest bearing.

         Payments of management fees and reimbursed expenses were deferred in
prior years pursuant to restrictions in the Partnership's note payable
agreement. The cumulative amount deferred was approximately $1,081,300. On
September 30, 1997, the Partnership obtained new financing and subsequently used
such borrowings and other available cash to pay $619,000 of previously deferred
management fees and reimbursed expenses. The remainder of these deferred
amounts, $462,300, was contributed as an equity contribution by the General
Partner to Enstar Finance Company, LLC ("EFC"), a subsidiary of the General
Partner, and remains an outstanding obligation of the Partnership. In the normal
course of business, the Partnership pays interest and principal to EFC, its
primary lender.

         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 $9,400



                                      -6-
<PAGE>   7
                       ENSTAR INCOME PROGRAM 1984-1, L.P.

                     NOTES TO CONDENSED FINANCIAL STATEMENTS

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


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

and $17,700 in the three and six months ended June 30, 1998. 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.

         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 $286,400 and $577,700
for the three and six months ended June 30, 1998. 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 have been allocated 99% to the Limited
Partners and 1% to the General Partner. The General Partner does not own units
of partnership interest in the Partnership, but rather holds a participation
interest in the income, losses and distributions of the Partnership.



                                      -7-
<PAGE>   8
                       ENSTAR INCOME PROGRAM 1984-1, 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 decreased from $1,331,700 to $1,317,300, or
by 1.1%, and from $2,700,600 to $2,647,300, or by 2.0% for the three and six
months ended June 30, 1998 as compared to the corresponding periods in 1997. Of
the $14,400 decrease in revenues for the three months ended June 30, 1998 as
compared to the corresponding period in 1997, $77,100 was due to decreases in
the number of subscriptions for basic, premium, tier and equipment rental
services. The decrease was partially offset by a $58,000 increase due to
increases in regulated service rates that were implemented by the Partnership in
1997 and a $4,700 increase in other revenue producing items. Of the $53,300
decrease in revenues for the six months ended June 30, 1998 as compared to the
corresponding period in 1997, $163,000 was due to decreases in the number of
subscriptions for basic, premium, tier and equipment rental services. The
decrease was partially offset by a $95,100 increase due to increases in
regulated service rates that were implemented by the Partnership in 1997 and a
$14,600 increase in other revenue producing items. As of June 30, 1998, the
Partnership had approximately 11,100 basic subscribers and 4,500 premium service
units.



                                      -8-
<PAGE>   9
                       ENSTAR INCOME PROGRAM 1984-1, L.P.


RESULTS OF OPERATIONS (CONTINUED)

         Service costs decreased from $484,200 to $466,500, or by 3.7%, and from
$979,400 to $946,500, or by 3.4%, for the three and six months ended June 30,
1998 as compared to the corresponding periods in 1997. Service costs represent
costs directly attributable to providing cable services to customers. The
decreases were principally due to lower copyright fees and programming expense.
Copyright fees decreased due to decreases in revenues as described above.
Programming expense decreased as a result of decreases in the number of
subscribers to certain premium channels.

         General and administrative expenses decreased from $265,200 to $177,400
or by 33.1%, and from $462,500 to $358,300, or by 22.5%, for the three and six
months ended June 30, 1998 as compared to the corresponding periods in 1997. The
decreases were primarily due to reductions in bad debt expense and personnel
costs. Personnel costs decreased primarily due to reduced expenses allocated by
an affiliate of the General Partner that discontinued management of the
Partnership's Tennessee operations in the fourth quarter of 1997. Such services
are now being provided by the General Partner.

         Management fees and reimbursed expenses increased from $142,300 to
$169,500, or by 19.1%, and from $280,800 to $337,000, or by 20.0%, for the three
and six months ended June 30, 1998 as compared to the corresponding periods in
1997. Management fees decreased by $700 and $2,600 for the three and six months
ended June 30, 1998 as compared to the corresponding periods in 1997, in direct
relation to decreased revenues as described above. Reimbursed expenses allocated
by the General Partner increased by $27,900 and $58,800 for the three and six
month periods as a result of transferring system operating management of the
Partnership's Tennessee systems from an affiliate to the General Partner.

         Depreciation and amortization expense increased from $139,800 to
$182,400, or by 30.5%, and from $276,300 to $360,800, or by 30.6%, for the three
and six months ended June 30, 1998 as compared to the corresponding periods in
1997. The increases were primarily due to asset additions.

         Operating income increased from $300,200 to $321,500, or by 7.1%, and
decreased from $701,600 to $644,700, or by 8.1%, for the three and six months
ended June 30, 1998 as compared to the corresponding periods in 1997. The three
months' increase was primarily due to lower bad debt expense and copyright fees.
The six months' decrease was principally the result of decreases in revenues and
increases in depreciation and amortization expense and reimbursed expenses as
described above.

         Interest income decreased from $7,500 to $7,300, or by 2.7%, and from
$19,100 to $11,800, or by 38.2%, for the three and six months ended June 30,
1998 as compared to the corresponding periods in 1997. The decreases were due to
lower cash balances available for investment.

         Interest expense decreased from $45,900 to $28,000, or by 39.0%, and
from $74,900 to $55,600, or by 25.8%, for the three and six months ended June
30, 1998 as compared to the corresponding periods in 1997, due to lower average
borrowings and lower average interest rates in the 1998 periods.

         Due to the factors described above, the Partnership's net income
increased from $261,800 to $300,800, or by 14.9%, and decreased from $645,800 to
$600,900, or by 7.0%, for the three and six months ended June 30, 1998 as
compared to the corresponding periods in 1997.



                                      -9-
<PAGE>   10
                       ENSTAR INCOME PROGRAM 1984-1, L.P.


RESULTS OF OPERATIONS (CONTINUED)

         Based on its experience in the cable television industry, the
Partnership believes that operating income before depreciation and amortization
(EBITDA) and related measures of cash flow serve as important financial analysis
tools for measuring and comparing cable television companies in several areas,
such as liquidity, operating performance and leverage. EBITDA is not a
measurement determined under generally accepted accounting principles ("GAAP")
and does not represent cash generated from operating activities in accordance
with GAAP. EBITDA should not be considered by the reader as an alternative to
net income as an indicator of financial performance or as an alternative to cash
flows as a measure of liquidity. In addition, the definition of EBITDA may not
be identical to similarly titled measures used by other companies. EBITDA as a
percentage of revenues increased from 33.0% to 38.3% and from 36.2% to 38.0%
during the three and six months ended June 30, 1998 as compared to the
corresponding periods in 1997. The increases were primarily due to decreases in
copyright fees and bad debt expense as described above. EBITDA increased from
$440,000 to $503,900, or by 14.5%, and from $977,900 to $1,005,500, or by 2.8%,
during the three and six months ended June 30, 1998 as compared to the
corresponding periods 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. In general, these
requirements involve expansion, improvement and upgrade of the Partnership's
existing cable systems and were $478,600 in the first six months of 1998. As of
the date of this Report, substantially all of the available channel capacity in
the Partnership's cable television systems is being utilized and each of such
systems requires an upgrade. The entire upgrade program is presently estimated
to require aggregate capital expenditures of approximately $8,000,000 and covers
12 franchise areas. These upgrades are currently required in five existing
franchise agreements. The upgrades required by the five existing franchise
agreements are estimated to cost approximately $3,400,000 and must be completed
by December 2001 and February 2002.

         On September 30, 1997, the Partnership entered into a loan agreement
with EFC for a revolving loan facility of $7,481,700 (the "Facility") of which
$250,000 was advanced to the Partnership at closing. The Partnership prepaid its
outstanding borrowings of $250,000 on June 22, 1998, although the Partnership's
management expects to reborrow under the Facility in the future 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 June 30, 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
June 30, 1998.



                                      -10-
<PAGE>   11
                       ENSTAR INCOME PROGRAM 1984-1, L.P.


LIQUIDITY AND CAPITAL RESOURCES (CONTINUED)

         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, due to the upgrade program discussed above, the
General Partner believes it is critical to conserve cash and borrowing capacity
and, consequently, has concluded that it would not be 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 65% of the Partnership's
subscribers are served by its system in Brownsville, Tennessee and neighboring
communities. Significant damage to the system due to seasonal weather 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 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 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 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 Partnership is
currently assessing its exposure to risks associated with its operating and
revenue generating equipment and has also initiated communications with
significant 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. The
Partnership currently expects that the cost to replace non-compliant equipment
will be determined during the third quarter of 1998. Such costs will be borne by
the Partnership. There can be no assurance that the systems of other companies



                                      -11-
<PAGE>   12
                       ENSTAR INCOME PROGRAM 1984-1, L.P.

LIQUIDITY AND CAPITAL RESOURCES (CONTINUED)

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 business.
The Partnership continues to closely monitor developments with its vendors and
service suppliers.

         SIX MONTHS ENDED JUNE 30, 1998 AND 1997

         Operating activities provided $143,000 less cash in the six months
ended June 30, 1998 than in the corresponding period in 1997. The Partnership
used $169,600 more cash for accounts payable due to differences in timing of
payments. Changes in accounts receivable, prepaid expenses and other assets
provided $17,000 more cash in the first six months of 1998 due to differences in
the timing of receivable collections and in the payment of prepaid expenses.

         The Partnership used $160,000 more cash in investing activities in the
six months ended June 30, 1998 than in the corresponding period of 1997, due to
a $182,700 increase in expenditures for tangible assets, partially offset by a
$22,700 decrease in spending for intangible assets.

         Financing activities provided $699,400 more cash in the six months
ended June 30, 1998 than in the comparable 1997 period. The Partnership used
$792,800 less cash for the repayment of debt and $89,400 more cash to pay
liabilities owed to the General Partner and other affiliates. The Partnership
used $4,000 more cash for the payment of deferred loan costs in the 1998 period.

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 the Partnership is able to increase its service
rates periodically, of which there can be no assurance.



                                      -12-
<PAGE>   13
                       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)      Exhibit 10.28 - Franchise Ordinance thereto
                           granting a non-exclusive community antenna
                           television franchise for the Town of
                           Grifton, North Carolina.

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



<PAGE>   14

                                   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:  August 13, 1998                 By:    /s/ Michael K. Menerey
                                              ----------------------------------
                                              Michael K. Menerey,
                                              Executive Vice President,
                                              Chief Financial Officer and
                                              Secretary
<PAGE>   15
                       ENSTAR INCOME PROGRAM 1984-1, L.P.


                                  EXHIBIT INDEX


<TABLE>
<CAPTION>
Exhibit
Number                                    Description
<S>               <C>
10.28             Franchise Ordinance thereto granting a non-exclusive community
                  antenna television franchise for the Town of Grifton, North 
                  Carolina.
</TABLE>



                                      E-1