<PAGE>
                                                                   EXHIBIT 10.21


THIS NOTE AND THE SHARES OF COMMON STOCK, PAR VALUE $0.01 PER SHARE, ISSUABLE
UPON CONVERSION HEREOF (COLLECTIVELY, THE "SECURITIES") REPRESENTED BY THIS
CERTIFICATE HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933 (THE
"SECURITIES ACT"), OR APPLICABLE STATE SECURITIES LAWS AND MAY NOT BE OFFERED,
SOLD, PLEDGED, HYPOTHECATED, TRANSFERRED OR OTHERWISE DISPOSED OF, UNLESS (I)(A)
A REGISTRATION STATEMENT COVERING SUCH SECURITIES IS EFFECTIVE UNDER THE
SECURITIES ACT AND (I)(B) APPLICABLE STATE SECURITIES LAWS HAVE BEEN COMPLIED
WITH, OR (II)(A) THE TRANSACTION IS EXEMPT FROM REGISTRATION UNDER THE
SECURITIES ACT, (II)(B) APPLICABLE STATE SECURITIES LAWS HAVE BEEN COMPLIED WITH
OR AN EXEMPTION FROM SUCH LAWS HAS BEEN MET AND (II)(C) IF THE OBLIGORS SO
REQUEST, A WRITTEN OPINION FROM COUNSEL (WHICH COUNSEL AND OPINION SHALL BE
SATISFACTORY TO THE OBLIGORS) THAT THE CONDITIONS IN (II)(A) AND (II)(B) ABOVE
HAVE BEEN SATISFIED.

THE SECURITIES REPRESENTED BY THIS NOTE ARE SUBJECT TO CERTAIN RESTRICTIONS ON
TRANSFER PURSUANT TO AN AGREEMENT AMONG THE NAMED PAYEE AND THE OBLIGORS. A COPY
OF THE AGREEMENT MAY BE OBTAINED FROM THE OBLIGORS AT THEIR PRINCIPAL OFFICE,
110 EAST 59TH STREET, NEW YORK, NEW YORK 10022.

                 10.75% UNSECURED CONVERTIBLE PIK NOTE DUE 2011

Dated: October 15, 2001                                     $833,125


      CoreComm Holdco, Inc., a Delaware corporation ("CoreComm HoldCo") and
CoreComm Limited, a Delaware corporation ("CoreComm" and together with CoreComm
HoldCo, the "Obligors"), hereby, jointly and severally, promise to pay to NTL
Incorporated, a Delaware corporation (the "Initial Holder"), or its registered
and permitted assigns (the "Holder"), the principal amount of Eight Hundred
Thirty-Three Thousand One Hundred Twenty-Five Dollars ($833,125) in U.S.
currency, on April 12, 2011 (the "Maturity Date"), to the extent the principal
amount hereof has not been converted or repaid, subject to the further
provisions of this Note set forth herein which further provisions shall for all
purposes have the same effect as if set forth at this place.

      Interest Payment Dates: October 15 and April 15, commencing April 15, 2002

      Definitions. For purposes of this Note, the following terms shall have the
meanings indicated:

      "Affiliate" means, with respect to any specified Person, any other Person
that directly, or indirectly through one or more intermediaries, controls, is
controlled by, or is under common control with such specified Person.

      "Agreement" shall mean the letter agreement entered into by and among
CoreComm, CoreComm Holdco and the Initial Holder, dated April 12, 2001, with
respect to the issuance of this Note and other commercial arrangements.

      "Board of Directors" shall mean the board of directors of CoreComm. "Board
of Directors" shall also mean the Executive Committee, if any, of such board of
directors or any other committee duly authorized by such board of directors to
perform any of its responsibilities with respect to this Note.

      "Business Day" shall mean any day other than a Saturday, Sunday or a day
on which state or federally chartered banking institutions in New York, New York
are not required to be open.

      "Change of Control" shall mean:
<PAGE>
                        -     the sale, lease or transfer of all or
                              substantially all of the assets of CoreComm to any
                              "person" or "group", within the meaning of
                              Sections 13(d)(3) and 14(d)(2) of the Exchange Act
                              or any successor provision to either of the
                              foregoing, including any group acting for the
                              purpose of acquiring, holding or disposing of
                              securities within the meaning of Rule 13d-5(b)(1)
                              under the Exchange Act, other than any Permitted
                              Holder;

                        -     any "person" or "group", within the meaning of
                              Sections 13(d)(3) and 14(d)(2) of the Exchange Act
                              or any successor provision to either of the
                              foregoing, including any group acting for the
                              purpose of acquiring, holding or disposing of
                              securities within the meaning of Rule 13d-5(b)(1)
                              under the Exchange Act, other than any Permitted
                              Holder, becomes the "beneficial owner", as defined
                              in Rule 13d-3 under the Exchange Act, of more than
                              50% (or more than 25% if neither George S.
                              Blumenthal or Barclay Knapp is an executive
                              officer of CoreComm at such time) of the total
                              voting power of all classes of the voting stock of
                              CoreComm and/or warrants or options to acquire
                              such voting stock of CoreComm, calculated on a
                              fully diluted basis, unless, as a result of such
                              transaction, the ultimate direct or indirect
                              ownership of CoreComm is substantially the same
                              immediately after such transaction as it was
                              immediately prior to such transaction; or

                        -     during any period of two consecutive years,
                              individuals who at the beginning of such period
                              constitute the Board of Directors, together with
                              any new directors whose election or appointment by
                              the Board of Directors or whose nomination for
                              election by the stockholders of CoreComm was
                              approved by a vote of a majority of the directors
                              then in office who were either directors at the
                              beginning of such period or whose election or
                              nomination for election was previously so
                              approved, cease for any reason to constitute a
                              majority of the Board of Directors then in office.

      "Common Stock" shall mean CoreComm's voting common stock, par value $0.01
per share, existing on the Issue Date or one or more classes of common stock or
other securities (including but not limited to tracking stock) of CoreComm as
such stock may be constituted or converted from time to time.

      "Conversion Price" shall mean the greater of (x) a 20.0% premium to the
25-Day Average Market Price of the Common Stock on the date of issuance of such
PIK Note and (y) $1.00; provided that if (x) and (y) are equal then the
conversion price shall be (x).

      "Current Market Price" of publicly traded shares of Common Stock or any
other class of capital stock or other security of CoreComm or any other issuer
for any day shall mean the last reported sale price for such security on the
principal exchange or quotation system on which such security is listed or
traded as of the close of the applicable regular trading hours for such Trading
Day, or if such day is not a Trading Day, the last reported sale price for such
security on such principal exchange or quotation system as of the close of the
applicable regular trading hours for the immediately preceding Trading Day. If
the security is not admitted for trading on any national securities exchange or
the Nasdaq National Market, "Current Market Price" for any day shall mean the
average of the last reported closing bid and asked prices reported by the Nasdaq
for such day as furnished by any member in good standing of the National
Association of Securities Dealers, Inc., selected from time to time by CoreComm
for that purpose or as quoted by the National Quotation Bureau Incorporated. In
the event that no such quotation is available for such day, the Current Market
Price shall be the average of the quotations for the last five Trading Days for
which a quotation is available within the last thirty Trading Days prior to such
day. In the event that five such quotations are not available within such
thirty-Trading Day period, the Board of Directors shall be entitled


                                       2
<PAGE>
to determine the Current Market Price on the basis of such quotations as it
reasonably considers appropriate.

      "DTC" shall have the meaning set forth in Exhibit A-1 hereto.

      "DWAC Transfer" shall have the meaning set forth in Exhibit A-1 hereto.

      "Exchange Act" shall mean the Securities Exchange Act of 1934, as amended,
and the rules and regulations promulgated thereunder.

      "Issue Date" shall mean the date on which this Note was first issued by
the Obligors.

      "Nasdaq" means the Nasdaq Stock Market, Inc., the electronic securities
market regulated by the National Association of Securities Dealers, Inc.

      "Nasdaq National Market" shall have the meaning set forth in Rule
4200(a)(23) of the rules of the National Association of Securities Dealers, Inc.

      "NYSE" means the New York Stock Exchange.

      "outstanding" when used with reference to shares of capital stock, shall
mean issued shares, excluding shares held by CoreComm or a subsidiary of
CoreComm.

      "Permitted Designee" shall mean: (1) a spouse or child of a Permitted
Holder, (2) trusts for the benefit of a Permitted Holder or a spouse or child of
a Permitted Holder, (3) in the event of the death or incompetence of a Permitted
Holder, his estate, heirs, executor, administrator, committee or other personal
representative or (4) any Person, so long as a Permitted Holder owns at least
50% of the voting power of all classes of the voting stock of such Person.

      "Permitted Holders" shall mean George S. Blumenthal, Barclay Knapp and
their Permitted Designees.

      "Person" shall mean any individual, partnership, association, joint
venture, corporation, business, trust, joint stock company, limited liability
company, any unincorporated organization, any other entity, a "group" of such
persons, as that term is defined in Rule 13d-5(b) under the Exchange Act, or a
government or political subdivision thereof.

      "Securities Act" shall mean the Securities Act of 1933, as amended, and
the rules and regulations promulgated thereunder.

      "Trading Day" shall mean any day on which the securities in question are
traded on the NYSE or, if such securities are not listed or admitted for trading
on the NYSE, on the principal national securities exchange on which such
securities are listed or admitted or, if not listed or admitted for trading on
any national securities exchange, on the Nasdaq National Market or, if such
securities are not quoted thereon, in the applicable securities market in which
the securities are traded.

      "25-Day Average Market Price" shall mean, for any security, the
volume-weighted average of the Current Market Prices of that security for the
twenty-five Trading Days immediately preceding the date of determination.

      Interest. This Note shall accrue interest at a rate of 10.75% per annum.
The Obligors jointly and severally promise to pay interest on this Note
semiannually on each October 15 and April 15, commencing on April 15, 2002 to
the registered Holder on the immediately preceding October 1 and April 1,
respectively. Interest on this Note shall be payable in kind by the issuance of
additional Notes (the "PIK Notes") in such principal amount as shall equal the
interest payment that is then due. The PIK Notes shall have terms substantially
identical to this Note. Interest on this Note shall accrue from the most recent
date to which interest has been paid, or if no interest has been paid, from
October 15, 2001. Interest shall be computed on the basis of a 360-day year
consisting of twelve thirty-day months. The Obligors shall pay


                                        3
<PAGE>
interest on overdue principal at the interest rate borne by this Note,
compounded semiannually, and the Obligors shall pay interest on overdue
installments of interest at the same interest rate compounded semiannually.

      Payment of Interest. The Obligors shall pay interest on this Note to the
registered Holder on the record date for the next interest payment date even
though this Note is canceled or redeemed after the record date and on or before
the applicable interest payment date.

      Ranking. This Note and the PIK Notes shall rank as a senior debt
obligation of CoreComm Holdco. This Note and the PIK Notes shall rank as a
subordinated debt obligation of CoreComm.

      Optional Redemption. This Note is not redeemable at the Obligors' option
prior to April 12, 2003. Thereafter, this Note shall be subject to redemption at
the option of the Obligors, in whole or in part, in U.S. currency, upon not less
than thirty days' prior written notice, at the redemption prices (expressed as
percentages of principal amount thereof) set forth below, plus accrued and
unpaid interest thereon to the applicable redemption date, if redeemed during
the twelve-month period beginning on April 12 of the years indicated below:

<TABLE>
<CAPTION>
                    Year                       Percentage
                    ----                       ----------
<S>                                            <C>
                    2003                        103.429%
                    2004                        102.571%
                    2005                        101.714%
                    2006                        100.857%
                    2007 and thereafter         100.000%
</TABLE>

      In the event the Obligors elect to redeem any of the outstanding principal
amount of 10.75% Senior Unsecured Convertible PIK Notes due 2010 issued and sold
to certain members of the Board of Directors and senior management of CoreComm
in December, 2000, or of any PIK Notes issued by the Obligors as interest
thereunder, all as amended from time to time (collectively the "Management PIK
Notes"), Obligors shall send written notice to Holder of such election to redeem
such principal amount at least thirty days prior to any such redemption. Holder
shall have the right by written notice to Obligors, made within thirty days
after receipt of such notice of such election to redeem, to require Obligors to
redeem this Note and the PIK Notes held by the Holder on the same terms and on a
pro rata basis with the Management PIK Notes, subject to compliance with federal
and state securities laws; provided that the applicable redemption price of this
Note and PIK Notes shall be as provided above as of the applicable redemption
date. The Obligors shall pay any redemption obligation in U.S. currency any and
all interest accrued and unpaid on this Note and the PIK Notes as of the date of
redemption.

      Procedure for Redemption. If the Obligors shall elect to redeem any
principal amount of this Note, notice of such redemption shall be given by
certified mail, return receipt requested, postage prepaid, mailed not less than
thirty days prior to the redemption date, to the Holder at such holder's address
as the same appears on the books and records of the Obligors and confirmed by
facsimile transmission on the date of such notice to the Holder if the Obligors
have been furnished with a facsimile number by the Holder; provided, however,
that neither the failure to give such notice nor confirmation nor any defect
therein or in the mailing thereof, to any particular Holder, shall affect the
sufficiency of the notice or the validity of the proceedings for redemption with
respect to any other Holder. Any notice that was mailed in the manner herein
provided and confirmed by facsimile transmission on the date of such notice if
the Obligors have been furnished with a facsimile number by the Holder shall be
conclusively presumed to have been duly given on the date mailed whether or not
the Holder actually receives the notice. Each such notice shall state: (1) the
redemption date; (2) the principal amount of this Note to be redeemed and, if
less than the principal amount held by the Holder is to be redeemed, the
principal amount to be redeemed from the Holder; (3) the amount payable in cash;
and (4) the place where this Note is to be surrendered for payment.

      If notice has been mailed as aforesaid and confirmed by facsimile
transmission on the date of such notice, from and after the applicable
redemption date (unless default shall be made by the Obligors in providing for
the payment of the redemption price of the principal amount called for
redemption together


                                       4
<PAGE>
with accrued and unpaid interest), (1) except as otherwise provided herein,
interest on the principal amount of this Note so called for redemption shall
cease to accrue and (2) all rights of the Holder as a holder of this Note shall
cease, except the right to receive from the Obligors the redemption price in
cash, upon surrender and endorsement of this Note.

      Notwithstanding any other provision of this Note, any redemption initiated
by the Obligors with respect to any outstanding principal amount of this Note
shall be suspended for one period of up to ninety (90) days (from and after the
applicable redemption date) per redemption initiated by the Obligors (the
"Tolling Period") solely for the purpose of the Holder satisfying any applicable
legal and regulatory approvals required to effect conversion of any outstanding
principal amount of this Note (and any accrued and unpaid interest thereon), and
during such period any redemption initiated by the Obligors with respect to any
outstanding principal amount of this Note (and any accrued and unpaid interest
thereon), shall have no force and effect, as to any outstanding principal amount
of this Note (and any accrued and unpaid interest thereon), which the Holder
shall elect to convert to Common Stock by delivery to CoreComm of a notice of
election to convert in the form of Exhibit A-1 to this Note (a "Notice of
Conversion") completed and signed, specifying the principal amount of this Note
to be converted at least five Business Days prior to the applicable redemption
date designated by the Obligors by notice of redemption to the Holder.

      The Obligors and the Initial Holder (and any subsequent Holder as a
condition to their receipt of any principal amount under this Note by purchase,
set-off, gift, bequeath or other manner of transfer or assignment, whether or
not for value), attempting to effect conversion subsequent to the Obligors
taking action to redeem this Note, mutually covenant and agree to promptly make
any and all filings (including requests for additional information), and
appearances, and to take any and all other actions necessary to secure legal and
regulatory approval to effect conversion of the principal amount of this Note so
requested. In the event that at the expiration of the Tolling Period any
applicable legal and regulatory approvals required to effect conversion of the
principal amount of this Note so requested have not been secured as a direct
result of the Obligors not complying with their obligations in the first
sentence of this paragraph, the Tolling Period shall be extended (the "Extended
Tolling Period) (through no action on the part of the Holder) until such
applicable legal and regulatory approvals shall have been obtained, or until it
shall have been finally determined by the applicable authority that any such
legal and regulatory approval shall not be available, but such Extended Tolling
Period shall in no event extend beyond sixty days after the expiration of the
Tolling Period unless the Obligors fail or refuse during such Extended Tolling
Period to comply with their obligations under the first sentence of this
paragraph. The Tolling Period or Extended Tolling Period (as applicable) shall
cease in the event that the Holder has not complied with its obligations in the
first sentence of this paragraph after written notice of such non-compliance by
the Obligors to the Holder by certified mail return receipt requested, and
failure by the Holder to come into compliance with its obligations under the
first sentence of this paragraph within ten Business Days after the date of such
notice. In the event the Holder shall not within such time period have come into
full compliance with its obligations under the first sentence of this paragraph,
the Obligors shall be permitted to immediately effect such redemption.

      Mandatory Redemption. Except as set forth above under the section
"Optional Redemption", the Obligors shall not be required to make mandatory
redemption or repurchase payments with respect to this Note prior to the
Maturity Date. There are no sinking fund payments with respect to this Note.

      Conversion. The Holder of this Note has the right, exercisable at any time
and from time to time prior to 5:00 p.m., Eastern Time, on April 12, 2011, to
convert the principal amount hereof (or any portion hereof that is an integral
multiple of $1,000.00 principal amount hereof) into shares of Common Stock at
the Conversion Price (the quotient of each integral multiple of $1,000.00
principal amount of this Note divided by the Conversion Price then in effect
shall equal the "Conversion Rate", which Conversion Rate shall initially equal
1,000.0 per $1,000.00 aggregate principal amount of this Note, subject to
adjustment under the circumstances set forth below), except that if a Note is
called for redemption, the conversion right shall terminate at 5:00 p.m.,
Eastern Time, on the Business Day immediately preceding the date fixed for
redemption, except as set forth above under the section "Procedure for
Redemption". To the extent that there exists any accrued and unpaid interest
attributable to the principal amount of this Note to be converted, at the time
of conversion the number of shares of Common Stock to be delivered by the


                                       5
<PAGE>
Obligors shall be increased in an amount equal to the quotient of such accrued
and unpaid interest as of the conversion date divided by 120% of the 25-Day
Average Market Price of the Common Stock as of such conversion date.

      To convert any principal amount and any accrued and unpaid interest
thereon, a Holder must (1) furnish a Notice of Conversion to the Obligors, (2)
surrender the endorsed Note to the Obligors and (3) pay any transfer or similar
tax, if required. The Notice of Conversion shall state that the Holder has
satisfied or will have satisfied prior to the issuance of shares of Common Stock
upon conversion of such principal amount, and any accrued and unpaid interest
thereon, any and all legal or regulatory requirements for conversion, including
compliance with the Securities Act, the Exchange Act and the Hart-Scott-Rodino
Antitrust Improvements Act of 1976, as amended (the "HSR Act").

      The Obligors shall each use their reasonable best efforts in cooperating
with such Holder to obtain such legal or regulatory approvals to the extent
their cooperation is necessary. Upon conversion, no adjustment or payment shall
be made for interest, except as provided above, but if the Holder surrenders
this Note for conversion after 5:00 p.m., Eastern Time, on the record date for
the payment of an installment of interest and prior to the opening of business
on the next interest payment date, then, notwithstanding such conversion, the
interest payable on such interest payment date shall be paid to the Holder of
this Note on such record date. Upon conversion of only a portion of the
outstanding principal amount of this Note, a new Note shall be issued
representing the unconverted portion of this Note so surrendered without cost to
the Holder. No fractional shares or scrip representing fractions of shares of
Common Stock shall be issued upon conversion of this Note. Instead of any
fractional interest in a share of Common Stock that would otherwise be
deliverable upon conversion of this Note, CoreComm shall round upward to
determine the whole number of shares of Common Stock issuable upon conversion of
this Note.

      The Conversion Rate shall be subject to adjustment from time to time as
follows:

            (1)   If CoreComm shall after the Issue Date (a) declare a dividend
or make a distribution on its Common Stock in shares of its Common Stock, (b)
subdivide its outstanding Common Stock into a greater number of shares, (c)
combine its outstanding Common Stock into a smaller number of shares or (d)
effect any reclassification of its outstanding Common Stock, including a
reclassification into one or more classes of Common Stock or other securities
(including, tracking stock), the Conversion Rate in effect on the record date
for such dividend or distribution, or the effective date of such subdivision,
combination or reclassification, as the case may be, shall be proportionately
adjusted so that the Holder thereafter surrendering for conversion any
outstanding principal amount of this Note shall be entitled to receive the
number and kind of shares of Common Stock (or other securities) that the Holder
would have owned or have been entitled to receive after the happening of any of
the events described above had such principal amount of this Note been converted
immediately prior to the record date in the case of a dividend or distribution
or the effective date in the case of a subdivision, combination or
reclassification. An adjustment made pursuant to this paragraph shall become
effective immediately after the opening of business on the Business Day next
following the record date (except as otherwise provided in this section) in the
case of a dividend or distribution and shall become effective immediately after
the opening of business on the Business Day next following the effective date in
the case of a subdivision, combination or reclassification. In the event that
after fixing a record date such dividend or distribution does not occur, the
Conversion Rate shall be readjusted to the Conversion Rate which would have been
in effect if such record date had not been fixed. Adjustments in accordance with
this paragraph shall be made whenever any event listed above shall occur.

      (2)   If CoreComm shall after the Issue Date fix a record date for the
issuance of rights or warrants (in each case, other than any Rights issued
pursuant to the stockholder rights plan as provided in the "Rights Plan" section
below) to all holders of Common Stock entitling them (for a period expiring
within forty-five days after such record date) to subscribe for or purchase
Common Stock (or securities convertible or exercisable into Common Stock) at a
price per share (or, in the case of a right or warrant to purchase securities
convertible or exercisable into Common Stock, having an effective exercise price
per share of Common Stock, computed on the basis of the maximum number of shares
of Common Stock issuable upon conversion or exercise of such convertible or
exercisable securities, as the case may be, plus


                                       6
<PAGE>
the amount of additional consideration payable, if any, to receive one share of
Common Stock upon conversion or exercise of such securities, as the case may be)
less than the 25-Day Average Market Price on the date on which such issuance was
declared or otherwise announced by CoreComm (the "Determination Date"), then the
Conversion Rate in effect at the opening of business on the Business Day next
following such record date shall be adjusted so that the Holder shall be
entitled to receive, upon the conversion of any principal amount of this Note,
the number of shares of Common Stock determined by multiplying (a) the
Conversion Rate in effect immediately prior to such record date by (b) a
fraction, the numerator of which shall be the sum of (i) the number of shares of
Common Stock outstanding on the close of business on the Determination Date and
(ii) the number of additional shares of Common Stock offered for subscription or
purchase pursuant to such rights or warrants (or in the case of a right or
warrant to purchase securities convertible or exercisable into Common Stock, the
aggregate number of additional shares of Common Stock into which the convertible
or exercisable securities so offered are initially convertible or exercisable),
and the denominator of which shall be the sum of (x) the number of shares of
Common Stock outstanding on the close of business on the Determination Date and
(y) the number of shares that the aggregate proceeds to CoreComm from the
exercise of such rights or warrants for Common Stock would purchase at such
25-Day Average Market Price on such date (or, in the case of a right or warrant
to purchase securities convertible or exercisable into Common Stock, the number
of shares of Common Stock obtained by dividing the aggregate exercise price of
such rights or warrants for the maximum number of shares of Common Stock
issuable upon conversion or exercise of such convertible or exercisable
securities, plus the aggregate amount of additional consideration payable, if
any, to convert or exercise such securities into Common Stock, by such 25-Day
Average Market Price). Such adjustment shall become effective immediately after
the opening of business on the Business Day next following such record date
(except as otherwise provided in this section). Such adjustment shall be made
successively whenever such a record date is fixed. In the event that after
fixing a record date such rights or warrants are not so issued, the Conversion
Rate shall be readjusted to the Conversion Rate which would then be in effect if
such record date had not been fixed. In determining whether any rights or
warrants entitle the holders of Common Stock to subscribe for or purchase shares
of Common Stock at less than such 25-Day Average Market Price, there shall be
taken into account any consideration received by CoreComm upon issuance and upon
exercise of such rights or warrants, the value of such consideration, if other
than cash, to be determined by the Board of Directors in good faith. If any
rights or warrants referred to in this paragraph shall expire unexercised after
the same shall have been distributed or issued by CoreComm (or, in the case of
rights or warrants to purchase securities convertible or exercisable into Common
Stock once exercised, the conversion or exercise right of such securities shall
expire), the Conversion Rate shall be readjusted at the time of such expiration
to the Conversion Rate that would have been in effect if no adjustment had been
made on account of the distribution or issuance of such expired rights or
warrants.

      (3)   If CoreComm shall fix a record date for the making of a distribution
to all holders of its Common Stock of evidences of its indebtedness, shares of
its capital stock or assets (excluding regular cash dividends or distributions
declared in the ordinary course by the Board of Directors and dividends payable
in Common Stock for which an adjustment is made pursuant to paragraph (1) of
this section) or rights or warrants (in each case, other than any Rights issued
pursuant to the stockholder rights plan as provided in the "Rights Plan" section
below) to subscribe for or purchase any of its securities (excluding those
rights and warrants issued to all holders of Common Stock entitling them (for a
period expiring within forty-five days after such record date) to subscribe for
or purchase Common Stock or securities convertible or exercisable into shares of
Common Stock, which rights and warrants are referred to and treated in the
immediately preceding paragraph) (any of the foregoing being hereinafter
referred to in this paragraph as the "Securities"), then in each such case the
Conversion Rate shall be adjusted so that the Holder shall be entitled to
receive, upon the conversion thereof, the number of shares of Common Stock
determined by multiplying (a) the Conversion Rate in effect immediately prior to
the close of business on such record date by (b) a fraction, the numerator of
which shall be the 25-Day Average Market Price per share of Common Stock on such
record date, and the denominator of which shall be the 25-Day Average Market
Price per share of Common Stock on such record date less the then-fair market
value (as determined by the Board of Directors in good faith) of the portion of
the assets, shares of its capital stock or evidences of its indebtedness so
distributed or of such rights or warrants applicable to one share of Common
Stock. Such adjustment shall be made successively whenever such a record date is
fixed. In the event that after fixing a record date such distribution is not so
made, the Conversion Rate shall be readjusted to the Conversion


                                       7
<PAGE>
Rate which would then be in effect if such record date had not been fixed. Such
adjustment shall become effective immediately at the opening of business on the
Business Day next following (except as otherwise provided in this section) the
record date for the determination of stockholders entitled to receive such
distribution. For the purposes of this paragraph, the distribution of a
Security, which is distributed not only to the holders of the Common Stock on
the date fixed for the determination of stockholders entitled to such
distribution of such Security, but also is distributed with each share of Common
Stock delivered to the Holder after such determination date, shall not require
an adjustment of the Conversion Rate pursuant to this paragraph; provided,
however, that on the date, if any, on which the Holder would no longer be
entitled to receive such Security with a share of Common Stock (other than as a
result of the termination of all such Securities), a distribution of such
Securities shall be deemed to have occurred and the Conversion Rate shall be
adjusted as provided in this paragraph (and such day shall be deemed to be "the
date fixed for the determination of stockholders entitled to receive such
distribution" and "the record date" within the meaning of the three preceding
sentences). If any rights or warrants referred to in this paragraph shall expire
unexercised after the same shall have been distributed or issued by CoreComm
(or, in the case of rights or warrants to purchase securities convertible or
exercisable into Common Stock once exercised, the conversion right of such
securities shall expire), the Conversion Rate shall be readjusted at the time of
such expiration to the Conversion Rate that would have been in effect if no
adjustment had been made on account of the distribution or issuance of such
expired rights or warrants.

      (4)   In case CoreComm shall, by dividend or otherwise, distribute to all
holders of its Common Stock cash in the amount per share that, together with the
aggregate of the per share amounts of any other cash distributions to all
holders of its Common Stock made within the twelve months preceding the date of
payment of such distribution and in respect of which no adjustment pursuant to
this paragraph (4) has been made exceeds 5.0% of the 25-Day Average Market Price
immediately prior to the date of declaration of such dividend or distribution
(excluding any dividend or distribution in connection with the liquidation,
dissolution or winding up of CoreComm, whether voluntary or involuntary, and any
cash that is distributed upon a merger, consolidation or other transaction for
which an adjustment pursuant to paragraph (8) of this section is made), then, in
such case, the Conversion Rate shall be adjusted so that the same shall equal
the rate determined by multiplying (a) the Conversion Rate in effect immediately
prior to the close of business on the Record Date (as defined below) for the
cash dividend or distribution by (b) a fraction, the numerator of which shall be
the Current Market Price of a share of Common Stock on the Record Date and the
denominator shall be such Current Market Price of a share of Common Stock less
the per share amount of cash so distributed during the twelve-month period
applicable to one share of Common Stock, such adjustment to be effective
immediately prior to the opening of business on the Business Day following the
Record Date; provided, however, that in the event the denominator of the
foregoing fraction is zero or negative, in lieu of the foregoing adjustment,
adequate provision shall be made so that the Holder shall have the right to
receive upon conversion, in addition to the shares of Common Stock to which the
Holder is entitled, the amount of cash the Holder would have received had the
Holder converted the principal amount of this Note at the beginning of the
twelve-month period. In the event that such dividend or distribution is not so
paid or made, the Conversion Rate shall again be adjusted to be the Conversion
Rate which would then be in effect if such dividend or distribution had not been
declared. Notwithstanding the foregoing, if any adjustment is required to be
made as set forth in this paragraph, the calculation of any such adjustment
shall include the amount of the quarterly cash dividends paid during the
twelve-month reference period only to the extent such dividends exceed on an
aggregate basis the regular quarterly cash dividends paid during the twelve
months preceding the twelve-month reference period. For purposes of this
paragraph, "Record Date" shall mean, with respect to any dividend or
distribution in which the holders of Common Stock have the right to receive
cash, the date fixed for determination of stockholders entitled to receive such
cash. In the event that at any time cash distributions to holders of Common
Stock are not paid equally on all series of Common Stock, the provisions of this
paragraph shall apply to any cash dividend or cash distribution on any series of
Common Stock otherwise meeting the requirements of this paragraph, and this
paragraph shall be deemed amended to the extent necessary so that any adjustment
required shall be made on the basis of the cash dividend or cash distribution
made on any such series.

      (5)   In case of the consummation of a tender or exchange offer (other
than an odd-lot tender offer) made by CoreComm or any subsidiary of CoreComm for
all or any portion of the outstanding shares of Common Stock to the extent that
the cash and fair market value (as determined in good faith by the


                                       8
<PAGE>
Board of Directors) of any other consideration included in such payment per
share of Common Stock at the last time (the "Expiration Time") tenders or
exchanges may be made pursuant to such tender or exchange offer (as amended)
exceed by more than 5.0%, with any smaller excess being disregarded in computing
the adjustment to the Conversion Rate provided in this paragraph, the first
reported sale price per share of the Common Stock on the Trading Day next
succeeding the Expiration Time, then the Conversion Rate shall be adjusted so
that the same shall equal the rate determined by multiplying the Conversion Rate
in effect immediately prior to the Expiration Time by a fraction the numerator
of which shall be the sum of (a) the fair market value (determined as aforesaid)
of the aggregate consideration payable to stockholders based on the acceptance
(up to any maximum specified in the terms of the tender or exchange offer) of
all shares validly tendered or exchanged and not withdrawn as of the Expiration
Time (the shares deemed so accepted, up to any such maximum, being referred to
as the "Purchase Shares") and (b) the product of the number of shares of Common
Stock outstanding (less any Purchase Shares) on the Expiration Time and the
first reported sale price of the Common Stock on the Trading Day next succeeding
the Expiration Time, and the denominator of which shall be the number of shares
of Common Stock outstanding (including any tendered or exchanged shares) on the
Expiration Time multiplied by the first reported sale price of the Common Stock
on the Trading Day next succeeding the Expiration Time, such adjustment to
become effective immediately prior to the opening of business on the Business
Day following the Expiration Time.

      (6)   No adjustment in the Conversion Rate shall be required unless such
adjustment would require a cumulative increase or decrease of at least 1.0% in
the Conversion Rate; provided, however, that any adjustment(s) that by reason of
this paragraph are not required to be made shall be carried forward and taken
into account in any subsequent adjustment(s) until made; and provided further
that any adjustment shall be required and made in accordance with this section
not later than such time as may be required in order to preserve the tax-free
nature of a distribution for United States income tax purposes to the Holder.
Notwithstanding any other provision of this Note, the Obligors shall not be
required to make any adjustment of the Conversion Rate for the issuance of any
shares of Common Stock pursuant to any plan providing for the reinvestment of
dividends or interest payable on securities of CoreComm and the investment of
additional optional amounts in shares of Common Stock under such plan. All
calculations relating to the conversion of this Note shall be made to the
nearest cent, rounded upward to the fifth decimal point or rounded upward to the
nearest share, as the case may be. Anything in this Note to the contrary
notwithstanding, CoreComm shall be entitled, to the extent permitted by law, to
make such adjustments in the Conversion Rate, in addition to those required by
this section, as it in its discretion shall determine to be advisable in order
that any stock dividends, subdivision of shares, reclassification or combination
of shares, distribution of rights or warrants to purchase stock or securities,
or a distribution of other assets (other than cash dividends) hereafter made by
CoreComm to its stockholders to the extent practicable shall not be taxable.

      (7)   In the event that, at any time as a result of shares of any other
class of capital stock becoming issuable in exchange or substitution for or in
lieu of shares of Common Stock or as a result of an adjustment made pursuant to
this section, the Holder upon subsequent conversion shall become entitled to
receive any shares of capital stock of CoreComm other than Common Stock, the
number of such other shares so receivable upon conversion of any principal
amount of this Note shall thereafter be subject to adjustment from time to time
in a manner and on terms as nearly equivalent as practicable to the provisions
contained herein.

      (8)   Subject to paragraph (10) below, if CoreComm shall be a party to a
Change of Control transaction and excluding any transaction as to which the
first paragraph of this section applies, in each case as a result of which
shares of Common Stock shall be converted into the right to receive stock,
securities or other property (including cash or any combination thereof), there
shall be no adjustment to the Conversion Rate but any principal amount of this
Note which is not converted into the right to receive stock, securities or other
property in connection with such Change of Control transaction shall thereafter
be convertible into the kind and amount of shares of stock, securities and other
property (including cash or any combination thereof) receivable upon the
consummation of such Change of Control transaction by a holder of that number of
shares of Common Stock into which the aggregate principal amount of this Note
would have been convertible into immediately prior to such Change of Control
transaction, assuming such holder of Common Stock (a) is not a Person with which
CoreComm consolidated or into which CoreComm


                                       9
<PAGE>
merged or which merged into CoreComm or to which such sale or transfer was made,
as the case may be (a "Constituent Person"), or an Affiliate of a Constituent
Person and (b) failed to exercise his rights of election, if any, as to the kind
or amount of stock, securities and other property (including cash) receivable
upon such Change of Control transaction (provided, that, if the kind or amount
of stock, securities and other property (including cash) receivable upon such
Change of Control transaction is not the same for each share of Common Stock
held immediately prior to such Change of Control transaction by other than a
Constituent Person or an Affiliate thereof and in respect of which such rights
of election shall not have been exercised (a "non-electing share"), then for the
purpose of this paragraph the kind and amount of stock, securities and other
property (including cash) receivable upon such Change of Control transaction by
each non-electing share shall be deemed to be the kind and amount so receivable
per share by a plurality of the non-electing shares). The provisions of this
paragraph shall similarly apply to successive Change of Control transactions.

      (9)   Notwithstanding anything in this Note to the contrary, if CoreComm
is reorganized such that the Common Stock is exchanged for the common stock of a
new entity ("Holdco") whose common stock is traded on the Nasdaq National Market
or a recognized securities exchange or automated quotation system, then the
Obligors by written notice to the Holder, may cause the exchange of this Note
for a new note having the same terms and conditions as set forth herein, except
as to joint obligors, subject to such rights effectively giving to Holder the
same economic rights as this Note (including for these purposes any resultant
changes in the tax treatment for the new note).

      (10)  Notwithstanding anything in this Note to the contrary, if a Change
of Control occurs, Holder shall have a one-time option, for a period of thirty
days following written notice from CoreComm, which written notice shall be given
not less than fifteen days prior to the expected occurrence of the Change of
Control, to convert the principal amount of this Note, and any accrued and
unpaid interest thereon, into shares of Common Stock at the Change of Control
Conversion Rate. The "Change of Control Conversion Rate" shall be equal to the
principal amount of this Note, and any accrued and unpaid interest thereon,
divided by the Special Conversion Price. The Change of Control Conversion Rate
shall be adjusted from time to time in accordance with the provisions of this
section applicable generally to adjustment of the Conversion Rate. Nothing in
this paragraph (10) is intended to limit or alter the conversion rights of the
Holder. For purposes of this paragraph (10), the following definitions shall
apply:

(a)   "SPECIAL CONVERSION PRICE" SHALL MEAN THE GREATER OF (x) 66.67% OF THE
25-DAY AVERAGE MARKET PRICE OF THE COMMON STOCK IMMEDIATELY PRECEDING THE RECORD
DATE FOR SUCH PIK NOTE ISSUANCE AND (y) THE CHANGE OF CONTROL PRICE (AS DEFINED
HEREIN).

(b)   "CHANGE OF CONTROL PRICE" SHALL MEAN (i) THE FAIR MARKET VALUE OF THE
CONSIDERATION THAT WOULD BE RECEIVED BY A HOLDER OF COMMON STOCK FOR ONE SHARE
OF COMMON STOCK IN A CHANGE OF CONTROL TRANSACTION FROM ANY SUCCESSOR, ACQUIROR
OR OTHER THIRD PARTY IF SUCH TRANSACTION WERE TO OCCUR ON THE DATE OF THE NOTICE
REFERRED TO IN THE FIRST SENTENCE OF THIS PARAGRAPH (10) OR (ii) THE ALTERNATIVE
CHANGE OF CONTROL PRICE IF THE HOLDERS OF COMMON STOCK DO NOT RECEIVE ANY
CONSIDERATION IN A CHANGE OF CONTROL TRANSACTION FROM ANY SUCCESSOR, ACQUIROR OR
OTHER THIRD PARTY. FOR PURPOSES OF THIS DEFINITION, "ALTERNATIVE CHANGE OF
CONTROL PRICE" SHALL MEAN THE FAIR MARKET VALUE PER SHARE OF COMMON STOCK ON THE
DATE OF THE NOTICE REFERRED TO IN THE FIRST SENTENCE OF THIS PARAGRAPH (10).

      (11)  Notwithstanding any other provision of this Note, the Initial Holder
or any Affiliate may from time to time elect to apply as the Conversion Rate
hereunder as to any principal amount of this Note the conversion rate then
applicable to the identical amount of principal and interest under any one or
more Management PIK Notes. CoreComm agrees to provide to the Initial Holder at
its request from time to time the conversion rate(s) then applicable under the
Management PIK Notes.

      Whenever the Conversion Rate is adjusted as herein provided, the Obligors
shall prepare an officer's certificate with respect to such adjustment of the
Conversion Rate setting forth the adjusted Conversion Rate and the effective
date of such adjustment and shall mail a copy of such officer's certificate to
the Holder at the Holder's last address as shown on the books and records of the
Obligors and confirm by facsimile transmission on the date of such notice to the
Holder if the Obligors have been furnished with


                                       10
<PAGE>
such facsimile address by the Holder. Any PIK Notes issued and delivered in
connection with the payment of semiannual interest on this Note shall contain
terms substantially identical to those contained in this section.

      In any case in which the foregoing paragraphs provide that an adjustment
shall become effective on the day next following a record date for an event,
CoreComm may defer until the occurrence of such event (a) issuing to the Holder
of any principal amount of this Note converted after such record date and before
the occurrence of such event the additional shares of Common Stock issuable upon
such conversion by reason of the adjustment contemplated by such event over and
above the Common Stock issuable upon such conversion before giving effect to
such adjustment and (b) paying to such holder any amount in cash in lieu of any
fraction of a share of Common Stock pursuant to this section.

      For purposes of this section, the number of shares of Common Stock at any
time outstanding shall not include any shares of Common Stock then owned or held
by or for the account of CoreComm or any subsidiary of CoreComm. CoreComm shall
not pay a dividend or make any distribution on shares of Common Stock held in
the treasury of CoreComm.

      If any single action would require adjustment of the Conversion Rate
pursuant to more than one paragraph of this section, only one adjustment shall
be made and such adjustment shall be the amount of adjustment that has the
highest absolute value.

      The value of any consideration received by CoreComm for the issuance of
any securities of CoreComm, if other than cash, shall be determined by the Board
of Directors in good faith, whose determinations shall be final and binding.

      If CoreComm shall take any action affecting the Common Stock, other than
actions described in this section, that in the opinion of the Board of Directors
materially adversely affects the conversion rights of the Holder, the Conversion
Rate may be adjusted by the Board of Directors, to the extent permitted by law,
in such manner, if any, and at such time, as the Board of Directors may
determine in good faith to be equitable in the circumstances; provided that the
provisions of this paragraph shall not affect any rights the Holder may have at
law or in equity.

      CoreComm covenants that it shall at all times reserve and keep available,
free from preemptive rights, out of the aggregate of its authorized but unissued
shares of Common Stock for the purpose of effecting conversion of this Note, the
full number of shares of Common Stock deliverable upon the conversion of the
entire outstanding principal amount of this Note. For purposes of this
paragraph, the number of shares of Common Stock that shall be deliverable upon
the conversion of the entire outstanding principal amount of this Note shall be
computed as if at the time of computation all such outstanding shares were held
by a single holder.

      CoreComm covenants that any shares of Common Stock initially issued upon
conversion of this Note shall be duly authorized, validly issued, fully paid and
non-assessable. Before taking any action that would cause an adjustment
increasing the Conversion Rate such that the quotient of the principal amount of
this Note and the Conversion Rate would be reduced below the then-par value of
the shares of Common Stock deliverable upon conversion of this Note, CoreComm
shall take any corporate action that, based on the opinion of its counsel, may
be necessary in order that CoreComm may validly and legally issue fully paid and
non-assessable shares of Common Stock with respect to such adjusted Conversion
Rate.

      Prior to the delivery of any securities that CoreComm shall be obligated
to deliver upon conversion of this Note, CoreComm shall be permitted to comply
with all applicable federal and state laws and regulations which require action
to be taken by CoreComm, including but not limited to compliance with the
Securities Act, the Exchange Act, the HSR Act, the rules and regulations of
Nasdaq (or any exchange or automated quotation system on which the Common Stock
is then listed or traded). The Obligors shall pay or cause to be paid the costs
and expenses of the Holder associated with such compliance.


                                       11
<PAGE>
      CoreComm shall pay any and all documentary stamp or similar issue or
transfer taxes payable in respect of the issue or delivery of shares of Common
Stock or other securities or property on conversion of this Note; provided,
however, that CoreComm shall not be required to pay any tax that may be payable
in respect of any transfer involved in the issue or delivery of shares of Common
Stock or other securities or property in a name other than that of the Holder to
be converted and no such issue or delivery shall be made unless and until the
Holder requesting such issue or delivery has paid to CoreComm the amount of any
such tax or established, to the satisfaction of CoreComm, that such tax has been
paid or satisfied in full.

      Loss, Theft, Mutilation or Destruction of Note. Upon receipt by the
Obligors of evidence of the loss, theft, destruction, or mutilation of this Note
and (in the case of loss, theft, or destruction) of indemnity satisfactory to
the Obligors, and upon surrender and cancellation of this Note, if mutilated,
the Obligors shall execute and deliver a new note on identical terms. Any Holder
making a request hereunder shall be responsible for all cost and expenses
associated therewith, including but not limited to the securing of an indemnity
bond.

      Standstill Restrictions.

      The Initial Holder agrees that, for a period beginning on the Issue Date
and ending on the date that a Change of Control is consummated:

(1)   THE INITIAL HOLDER AND ITS AFFILIATES SHALL NOT FORM, JOIN, PARTICIPATE IN
OR ENCOURAGE THE FORMATION OF A PARTNERSHIP, LIMITED PARTNERSHIP, SYNDICATE OR
OTHER GROUP FOR THE PURPOSE OF ACQUIRING, HOLDING OR DISPOSING OF ANY SECURITY
OF CORECOMM WHICH HAS VOTING RIGHTS ON MATTERS SUBMITTED TO ALL STOCKHOLDERS OF
CORECOMM ("VOTING SECURITIES"); PROVIDED, HOWEVER, FOR PURPOSES OF THIS SECTION,
THE HOLDER AND ITS AFFILIATES SHALL NOT BE CONSIDERED TO BE A SYNDICATE OR
GROUP;

(2)   THE INITIAL HOLDER AND ITS AFFILIATES SHALL NOT MAKE, OR IN ANY WAY
PARTICIPATE IN, DIRECTLY OR INDIRECTLY, ANY "SOLICITATION" OF "PROXIES" (AS SUCH
TERMS ARE DEFINED OR USED IN REGULATION 14A UNDER THE EXCHANGE ACT) OR BECOME A
"PARTICIPANT" IN ANY "ELECTION CONTEST") (AS SUCH TERMS ARE DEFINED OR USED IN
RULE 14a-11 UNDER THE EXCHANGE ACT) WITH RESPECT TO CORECOMM (OTHER THAN BY WAY
OF THE INITIAL HOLDER AND ITS AFFILIATES EXERCISING THEIR RIGHT TO VOTE VOTING
SECURITIES HELD BY THE INITIAL HOLDER AND ITS AFFILIATES), OR INITIATE, PROPOSE
OR OTHERWISE SOLICIT STOCKHOLDERS OF CORECOMM FOR THE APPROVAL OF ONE OR MORE
STOCKHOLDER PROPOSALS WITH RESPECT TO CORECOMM OR INDUCE OR ATTEMPT TO INDUCE
ANY OTHER PERSON TO INITIATE ANY STOCKHOLDER PROPOSAL;

(3)   THE INITIAL HOLDER AND ITS AFFILIATES SHALL NOT OTHERWISE ACT, DIRECTLY OR
INDIRECTLY, ALONE OR IN CONCERT WITH OTHERS, TO SEEK TO CONTROL THE MANAGEMENT,
BOARD OF DIRECTORS, POLICIES OR AFFAIRS OF CORECOMM OR ANY OF ITS SUBSIDIARIES,
OR SOLICIT, PROPOSE, SEEK TO EFFECT OR NEGOTIATE WITH ANY OTHER PERSON WITH
RESPECT TO ANY FORM OF BUSINESS COMBINATION TRANSACTION INVOLVING, DIRECTLY OR
INDIRECTLY, CORECOMM OR ANY OF ITS SUBSIDIARIES, OR ANY RESTRUCTURING,
RECAPITALIZATION OR SIMILAR TRANSACTION WITH RESPECT TO CORECOMM OR ANY OF ITS
SUBSIDIARIES, OR ANNOUNCE OR DISCLOSE AN INTENT, PURPOSE, PLAN OR PROPOSAL WITH
RESPECT TO CORECOMM OR ANY OF ITS SUBSIDIARIES OR ANY VOTING SECURITIES
INCONSISTENT WITH THE PROVISIONS OF THIS SECTION, INCLUDING AN INTENT, PURPOSE,
PLAN OR PROPOSAL THAT IS CONDITIONED ON OR WOULD REQUIRE CORECOMM TO WAIVE THE
BENEFIT OF OR AMEND ANY PROVISION OF THE AGREEMENT OR THIS NOTE, OR ASSIST,
PARTICIPATE IN, FACILITATE OR ENCOURAGE OR SOLICIT ANY EFFORT OR ATTEMPT BY ANY
PERSON TO DO OR SEEK TO DO ANY OF THE FOREGOING; AND

(4)   THE INITIAL HOLDER AND ITS AFFILIATES SHALL NOT ENCOURAGE OR RENDER ADVICE
TO OR MAKE ANY RECOMMENDATION OR PROPOSAL TO ANY PERSON, OR DIRECTLY OR
INDIRECTLY PARTICIPATE, AID OR ABET OR OTHERWISE INDUCE ANY PERSON OR ENGAGE IN
ANY OF THE ACTIONS PROHIBITED BY THIS SECTION OR TO ENGAGE IN ANY ACTIONS
CONSISTENT WITH SUCH PROHIBITIONS.

      Stockholder Rights Agreement. This Note shall be entitled to the benefits
of a number of rights issuable under the Rights Agreement, dated as of September
29, 2000, by and between CoreComm and Continental Stock Transfer & Trust Company
or any successor plan of similar purpose and effect (the "Rights") equal to the
number of shares of Common Stock then issuable upon conversion of this Note at
the


                                       12
<PAGE>
prevailing Conversion Rate. Any shares of Common Stock deliverable upon
conversion of this Note shall be accompanied by a Right.

      Amendments, Supplements and Waivers. This Note may be amended or
supplemented with the consent of the Holder (including consents obtained in
connection with a tender offer or exchange offer for this Note), and any
existing default may be waived with the consent of the Holder; provided that if
the Obligors propose to amend this Note to cure any immaterial ambiguity, defect
or inconsistency, or to make any change that does not adversely affect the
rights of the Holder, the consent of the Holder shall not be unreasonably
withheld or delayed. In the event that the Management PIK Notes are amended or
supplemented, CoreComm shall notify the Initial Holder in writing of such
amended or supplemented terms as soon as possible and offer to the Initial
Holder such terms in respect of this Note and the PIK Notes (including amending
this Note and the PIK Notes to reflect such revised terms); provided that if
CoreComm has not received written notification from the Initial Holder accepting
such amended or supplemented terms within ten Business Days of the Initial
Holder's receipt of such written notice from CoreComm, the Initial Holder shall
be deemed to have elected not to accept such amended or supplemented terms and
shall thereafter not have the benefit thereof, if any; provided that this right
does not apply to any principal amount of this Note and PIK Notes previously
converted or redeemed.

      NO RECOURSE AGAINST OTHERS. A DIRECTOR, OFFICER, EMPLOYEE, INCORPORATOR OR
STOCKHOLDER OF THE OBLIGORS, AS SUCH, SHALL NOT HAVE ANY LIABILITY FOR ANY
OBLIGATIONS OF THE OBLIGORS UNDER THIS NOTE OR FOR ANY CLAIM BASED ON, IN
RESPECT OF OR BY REASON OF SUCH OBLIGATIONS OR THEIR CREATION. THE HOLDER OF
THIS NOTE BY ACCEPTING A NOTE WAIVES AND RELEASES ALL SUCH LIABILITY. THE WAIVER
AND RELEASE ARE PART OF THE CONSIDERATION FOR THE ISSUANCE OF THIS NOTE.

      Notices. All consents, notices, documents, certificates, information and
legal process to be given under the terms of this Note shall be in writing and
(1) delivered personally, (2) sent by facsimile transmission, (3) sent by
registered or certified mail, postage prepaid or (4) sent by recognized
overnight courier to the applicable Person at the address stated below or in
accordance with the last unrevoked written direction from such Person. Unless
otherwise provided herein, all notices shall be deemed to have been given on (a)
the date of receipt (or if delivery refused, the date of such refusal) if
delivered personally or by recognized overnight courier, (b) three days after
the date of posting if sent by registered or certified mail, postage prepaid and
(c) if transmitted by facsimile, the date that confirmation of transmission is
received by the sending party. If to CoreComm or CoreComm Holdco, at: 110 East
59th Street, New York, New York 10022, attention: General Counsel, facsimile:
(212) 906-8497. If to the Holder, at its address and/or facsimile number on the
books and records of the Obligors.

      Assignability. This Note shall be binding upon the Obligors and their
successors and assigns and shall inure to the benefit of the Holder and its
successors and assigns. Assignment of this Note and the obligations hereunder by
either or both of the Obligors prior to the consummation of such assignment
shall require prior written consent of the Holder, unless the assignment (1) has
a bona fide business purpose in the reasonable judgment of a majority of the
members of (a) the Board of Directors and (b) the board of directors of CoreComm
Holdco or (2)(a) is to an Affiliate of one of the Obligors and (b) the Obligors
remain jointly and severally obligated under this Note. The securities
represented by this Note are subject to certain restrictions on transfer
pursuant to the Agreement. A copy of the Agreement may be obtained from the
Obligors at their principal office, 110 East 59th Street, New York, New York
10022.

      Remedies. Either the Obligors or the Holder (each a "non-defaulting
party") shall be entitled to resort to any and all remedies available at law or
in equity, including without limitation the remedy of specific performance, in
the event of a default by the other (the "defaulting party") which is not cured
within ten Business Days after written notice of such default by the
non-defaulting party to the defaulting party. In addition, in the event of the
default by Obligors under this Note which is not cured within ten Business Days
after written notice thereof by Holder, or in the event that either Obligor
shall voluntarily commence any proceeding or file any petition seeking
liquidation, reorganization or other relief under any federal or state
bankruptcy or insolvency law, or any such proceeding or petition is commenced or
filed on an involuntary basis with respect to either Obligor and any such
proceeding or petition shall continue undismissed for sixty days, then the
unpaid and unconverted portion of principal of this Note and accrued and unpaid
interest thereon shall at the option of the Holder be accelerated and shall be
immediately due in


                                       13
<PAGE>
full. In any proceeding to enforce any terms of this Note, the prevailing party
shall be entitled to recover its attorney's fees and costs in connection with
such proceeding.

      Denominations. Upon surrender and endorsement of this Note, the Obligors
shall issue a new Note to the Holder in the aggregate outstanding principal
amount hereof, in such denominations of at least $100,000.00 as the Holder shall
reasonably request in writing.

      Persons Deemed Owners. The registered Holder of this Note shall be treated
as its owner for all purposes, and the Obligors shall have no liability for
treating the registered Holder of this Note as its owner for all purposes.

      Governing Law. THE INTERNAL LAWS OF THE STATE OF NEW YORK SHALL GOVERN THE
NOTES WITHOUT REGARD TO CHOICE OF LAW OR CONFLICT OF LAW PROVISIONS THEREOF.


                                       14
<PAGE>
      IN WITNESS WHEREOF, each of the Obligors have caused this Note to be
signed manually or by facsimile by one of their duly authorized officers.

                                    CORECOMM LIMITED

                                    By: /s/ Michael A. Peterson
                                        ----------------------------------------
                                        Name: Michael A. Peterson
                                        Title:

                                    CORECOMM HOLDCO, INC.


                                    By: /s/ Thomas J. Gravina
                                        ----------------------------------------
                                        Name: Thomas J. Gravina
                                        Title:


                                       15
<PAGE>
                                                                     Exhibit A-1

                              NOTICE OF CONVERSION

            (To be Executed by the Holder of Principal Amount of the
                 10.75% Unsecured Convertible PIK Note Due 2011)

      The Holder hereby irrevocably elects to convert $______.00 principal
amount of 10.75% Unsecured Convertible PIK Note Due 2011, and any and all
accrued and unpaid interest thereon, into shares of Common Stock according to
the terms and conditions of the Note, as of the date written below. If
securities are to be issued in the name of a Person other than the undersigned,
the Holder shall pay all transfer taxes payable with respect thereto and is
delivering herewith the Note. No fee will be charged to the Holder for any
conversion, except for transfer taxes, if any.

      The Holder hereby represents and warrants that it has satisfied or will
have satisfied prior to the issuance of shares of Common Stock upon conversion
of the Note any and all legal and regulatory requirements for conversion,
including compliance with the Securities Act, the Exchange Act and the HSR Act.

      CoreComm shall electronically transmit the Common Stock issuable pursuant
to this Notice of Conversion to the account of the undersigned or its nominee
with The Depository Trust Company ("DTC") through its Deposit Withdrawal Agent
Commission System ("DWAC Transfer").

      Name of DTC Prime Broker:  _________________________

      Account Number:  ___________________________________

      [ ]   In lieu of receiving shares of Common Stock issuable pursuant to
            this Notice of Conversion by way of a DWAC Transfer, the undersigned
            hereby requests that CoreComm issue a certificate or certificates
            for the number of shares of Common Stock set forth above (which
            numbers are based on the Holder's calculation attached hereto) in
            the name(s) specified immediately below or, if additional space is
            necessary, on an attachment hereto:

      Name: ______________________________________________

      Address: ___________________________________________

      The Holder hereby represents and warrants that all offers and sales by the
Holder of the securities issuable to the Holder upon conversion of the Note
shall be made pursuant to registration of the securities under the Securities
Act and any applicable federal and state securities laws, or pursuant to an
applicable exemption from registration under the Securities Act and any
applicable state securities laws.

      Date of Conversion:  _______________________________
      Conversion Rate: ___________________________________

      Number of Shares of
      Common Stock to be Issued:  ________________________

      Signature:  ________________________________________
      Name:  _____________________________________________
      Address:  __________________________________________

*     CoreComm is not required to issue shares of Common Stock until the
      original Note to be converted (or evidence of loss, theft or destruction
      thereof) is received by CoreComm or CoreComm Holdco.