<PAGE>
 
                                                                     EXHIBIT 3.2



                                    BY-LAWS
                           Adopted January 21, 1997

<PAGE>
 
                                    BY-LAWS

                                      OF

                             CORECOMM INCORPORATED

                    (hereinafter called the "Corporation")

                                   ARTICLE I

                                    OFFICES
                                    -------

          Section 1.  Registered Office.  The registered office of the 
          ---------   -----------------
Corporation shall be in the City of Wilmington, County of New Castle, State of 
Delaware.

          Section 2.  Other Offices.  The Corporation may also have offices at 
          ---------   -------------
such other places both within and without the State of Delaware as the Board of
Directors may from time to time determine.


                                  ARTICLE II

                           MEETINGS OF STOCKHOLDERS
                           ------------------------

          Section 1.  Place of Meetings.  Meetings of the stockholders for the 
                      -----------------
election of directors or for any other purpose shall be held at such time and 
place, either within or without the State of Delaware as shall be designated 
from time to time by the Board of Directors and stated in the notice of the 
meeting or in a duly executed waiver of notice thereof.

          Section 2.  Annual Meetings.  Annual meetings of stockholders shall be
                      ---------------
held on such date and at such time as shall be designated from time to time by 
the Board of Directors and stated in the notice of the meeting, at which 
meetings the stockholders shall elect by a plurality vote a Board of Directors, 
and transact such other business as may properly be brought before the meeting 
in accordance with these By-laws. Written notice of the annual meeting stating 
the place, date and hour of the meeting shall be given to each stockholder 
entitled to vote at such meeting not less than ten nor more than sixty days 
before the date of the meeting.
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     Section 3.  Special Meetings.  Special meetings of stockholders, for any 
     ---------   ----------------
purpose or purposes, may be called by the Board of Directors, the Chairman of 
the Board of Directors or the President.  Special meetings of stockholders may 
not be called by any other person or persons.  Written notice of a special 
meeting stating the place, date and hour of the meeting and the purpose or 
purposes for which the meeting is called shall be given not less than ten nor 
more than sixty days before the date of the meeting to each stockholder entitled
to vote at such meeting, and only such business as is stated in such notice 
shall be acted upon thereat.

     Section 4.  Advance Notification of Business to be Transacted at 
                 ----------------------------------------------------
Stockholder Meetings.  To be properly brought before the annual or any special 
--------------------
stockholders' meeting, business must be either (a) specified in the notice of 
meeting (or any supplement or amendment thereto) given by or at the direction of
the Board of Directors, (b) otherwise properly brought before the meeting by or 
at the direction of the Board of Directors, or (c) otherwise properly brought 
before the meeting by a stockholder.  In addition to any other applicable 
requirements, for business to be properly brought before an annual or any 
special stockholders' meeting by a stockholder, the stockholder must have given 
timely notice thereof in writing to the secretary of the Corporation.  To be 
timely, a stockholder's notice must be delivered to or mailed and received at 
the principal executive offices of the Corporation not less than 75 days nor 
more than 90 days prior to the meeting; provided, however, that in the event 
that less than 90 days' notice or prior public disclosure of the date of the 
meeting is given or made to be so received not later than the close of business 
on the fifteenth day following the day on which such notice of the date of the 
meeting was mailed or such public disclosure was made, whichever first occurs.  
Such stockholder's notice to the Secretary shall set forth as to each matter the
stockholder proposes to bring before the meeting (i) a brief description of the 
business desired to be brought before the meeting and the reasons for conducting
such business at the meeting, (ii) the name and record address of the 
stockholder proposing such business, (iii) the class, series and number of 
shares of capital stock of the Corporation which are beneficially

                                       2
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owned by the stockholder and (iv) any material interest of the stockholder in 
such business.

     Notwithstanding anything in these By-laws to the contrary, no business 
shall be conducted at the annual or any special meeting except in accordance 
with the procedures set forth in this Article II, Section 4, provided, however, 
that nothing in this Section 5 shall be deemed to preclude discussion by any 
stockholder of any business properly brought before the meeting.  The officer of
the Corporation presiding at the meeting shall, if the facts warrant, determine 
and declare to the meeting that business was not properly brought before the 
meeting in accordance with the provisions of this Article II, Section 4, and if
he should so determine, he shall so declare to the meeting and any such business
not properly brought before the meeting shall not be transacted.

     Section 5.  Quorum.  Except as otherwise provided by law or by the 
     ---------
Certificate of Incorporation, the holders of a majority of the capital stock 
issued and outstanding and entitled to vote thereat, present in person or 
represented by proxy, shall constitute a quorum at all meetings of the 
stockholders for the transaction of business.  If, however, such quorum shall 
not be present or represented at any meeting of the stockholders, the 
stockholders entitled to vote thereat, present in person or represented by 
proxy, shall have power to adjourn the meeting from time to time, without notice
other than announcement at the meeting, until a quorum shall be present or 
represented.  At such adjourned meeting at which a quorum shall be present or 
represented, any business may be transacted wich might have been transacted at 
the meeting as originally noticed.  If the adjournment is for more than thirty 
days, or if after the adjournment a new record date is fixed for the adjourned 
meeting, a notice of the adjourned meeting shall be given to each stockholder 
entitled to vote at the meeting.

     Section 6.  Voting.  Unless otherwise required by law, the Certificate of 
                 ------
Incorporation or these By-laws, any question brought before any meeting of 
stockholders shall be decided by the vote of the holders of a majority of the 
stock represented and entitled to vote thereat.  Unless otherwise provided in 
the Certificate of Incorporation, each stockholder represented at a meeting of 
stockholders shall be entitled to cast one vote for

                                       3
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each share of the capital stock entitled to vote thereat held by such 
stockholder.  The Board of Directors, in its discretion, or the officer of the 
Corporation presiding at a meeting of stockholders, in his discretion, may 
require that any votes cast at such meeting shall be cast by written ballot.

     Section 7.  List of Stockholders Entitled to Vote.  The officer of the 
     ---------   -------------------------------------
Corporation who has charge of the stock ledger of the Corporation shall prepare 
and make, at least ten days before every meeting of stockholders, a complete 
list of the stockholders entitled to vote at the meeting, arranged in 
alphabetical order, and showing the address of each stockholder and the number 
of shares registered in the name of each stockholder.  Such list shall be open 
to the examination of any stockholder, for any purpose germane to the meeting, 
during ordinary business hours, for a period of at least ten days prior to the 
meeting, either at a place within the city where the meeting is to be held, 
which place shall be specified in the notice of the meeting, or, if not so 
specified, at the place where the meeting is to be held.  The list shall also be
produced and kept at the time and place of the meeting during the whole time 
thereof, and may be inspected by any stockholder of the Corporation who is 
present.

     Section 8.  Stock Ledger.  The stock ledger of the Corporation shall be the
     ---------   ------------
only evidence as to who are the stockholders entitled to examine the stock 
ledger, the list required by Section 7 of this Article II or the books of the 
Corporation, or to vote in person or by proxy at any meeting of stockholders.

                                  ARTICLE III

                                   DIRECTORS
                                   ---------

     Section 1.  Number and Election of Directors.  Subject to the rights, if 
                 --------------------------------
any, of holders of preferred stock of the Corporation, the Board of Directors 
shall consist of not less than three nor more than fifteen members, the exact 
number of which shall be fixed from time to time by the Board of Directors.  
Except as provided in Section 3 of this Article III, directors shall be elected 
by a plurality of the votes cast at Annual

                                       4
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Meetings of Stockholders, and each director so elected shall hold office as 
provided by Article FIFTH of the Certificate of Incorporation. Any director may
resign at any time upon written notice to the Corporation. Directors need not be
stockholders.

     Section 2.  Nomination of Directors.  Only persons who are nominated in 
     ---------   -----------------------
accordance with the following procedures shall be eligible for election as 
directors. Nominations of persons for election to the Board of Directors of the 
Corporation at the Annual Meeting may be made at such meeting by or at the 
direction of the Board of Directors, by any committee or persons appointed by
the Board of Directors or by any stockholder of the Corporation entitled to vote
for the election of directors at the meeting who complies with the notice
procedures set forth in this Article III, Section 2. Such nominations, other
than those made by or at the direction of the Board of Directors, shall be made
pursuant to timely notice in writing to the Secretary of the Corporation. To be
timely, a stockholder's notice must be delivered to or mailed and received at
the principal executive offices of the Corporation not less than 75 days nor
more than 90 days prior to the meeting; provided, however, that in the event
that less than 90 days' notice or prior public disclosure of the date of the
meeting is given or made to stockholders, notice by the stockholder to be timely
must be so received not later than the close of business on the fifteenth day
following the day on which such notice of the date of the meeting was mailed or
such public disclosure was made, whichever first occurs. Such stockholder's
notice to the Secretary shall set forth (a) as to each person whom the
stockholder proposes to nominate for election or re-election as a director, (i)
the name, age, business address and residence address of the person, (ii) the
principal occupation or employment of the person, (iii) the class, series and
number of shares of capital stock of the Corporation which are beneficially
owned by the person and (iv) any other information relating to the person that
is required to be disclosed in solicitations for proxies for election of
directors pursuant to the Rules and Regulations of the Securities and Exchange
Commission under Section 14 of the Securities Exchange Act of 1934, as amended;
and (b) as to the stockholder giving the notice (i) the name and record address
of the stockholder and (ii) the class, series and number of shares of capital
stock of the Cor-

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poration which are beneficially owned by the stockholder. Such notice shall be
accompanied by the executed consent of each nominee to serve as a director if so
elected. The Corporation may require any proposed nominee to furnish such other
information as may reasonably be required by the Corporation to determine the
eligibility of such proposed nominee to serve as a director of the Corporation.
No person shall be eligible for election as a director of the Corporation unless
nominated in accordance with the procedures set forth herein. The officer of the
Corporation presiding at an Annual Meeting shall, if the facts warrant,
determine and declare to the meeting that a nomination was not made in
accordance with the foregoing procedure, and if he should so determine, he
shall so declare to the meeting, and the defective nomination shall be
disregarded.

        Section 3. Vacancies. Any vacancy on the Board of Directors, howsoever 
        ---------  ---------
resulting, may be filled by a majority of the directors then in office, though 
less than a quorum, or by a sole remaining director. Any director elected to 
fill a vacancy shall hold office for a term that shall coincide with the term of
the class to which such director shall have been elected.

        Section 4. Duties and Powers. The business of the Corporation shall be 
        ---------  -----------------
managed by or under the direction of the Board of Directors which may exercise 
all such powers of the Corporation and do all such lawful acts and things as are
not by statute or by the Certificate of Incorporation or by these By-laws 
directed or required to be exercised or done by the stockholders.

        Section 5. Meetings. The Board of Directors of the corporation may hold 
        ---------  --------
meetings, both regular and special, either within or without the State of 
Delaware. Regular meetings of the Board of Directors may be held without notice 
at such time and at such place as may from time to time be determined by the 
Board of Directors. Special meetings of the Board of Directors may be called by 
the Chairman of the Board of Directors, the President or by a majority of the 
Board of Directors. Notice thereof stating the place, date and hour of the 
meeting shall be given to each director either by mail not less than forty-eight
(48) hours before the date of the meeting, or personally or by telephone, 
telegram, telex or similar means of communication on twenty-four (24) hours'


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notice, or on such shorter notice as the person or persons calling such meeting 
may deem necessary or appropriate in the circumstances.

     Section 6.  Quorum; Action of the Board of Directors.  Except as may be 
                 ----------------------------------------
otherwise specifically provided by law, the Certificate of Incorporation or 
these By-laws, at all meetings of the Board of Directors, a majority of the 
entire Board of Directors shall constitute a quorum for the transaction of 
business and the act of a majority of the directors present at any meeting at 
which there is a quorum shall be the act of the Board of Directors. If a quorum 
shall not be present at any meeting of the Board of Directors, the directors  
present thereat may adjourn the meeting from time to time, without notice other 
than announcement at the meeting, until a quorum shall be present.

     Section 7.  Action by Written Consent.  Any action required or permitted to
     ---------   -------------------------
be taken at any meeting of the Board of Directors or of any committee thereof 
may be taken without a meeting, if all the members of the Board of Directors or 
committee, as the case may be, consent thereto in writing, and the writing or 
writings are filed with the minutes of proceedings of the Board of Directors or 
committee.

     Section 8.  Meetings by Means of Conference Telephone.  Members of the 
     ---------   -----------------------------------------
Board of Directors of the Corporation, or any committee designated by the Board 
of Directors, may participate in a meeting of the Board of Directors or such 
committee by means of a conference telephone or similar communications equipment
by means of which all persons participating in the meeting can hear each other, 
and participation in a meeting pursuant to this Section 8 shall constitute 
presence in person at such meeting.

     Section 9.  Committees.  The Board of Directors may, by resolution passed 
     ---------   ----------
by a majority of the entire Board of Directors, designate one or more 
committees, each committee to consist of one or more of the directors of the 
Corporation. The Board of Directors may designate one or more directors as 
alternate members of any committee, who may replace any absent or disqualified 
member at any meeting of any such committee. In the absence or disqualification
of a member of a committee, and in the

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absence of a designation by the Board of Directors of an alternate member to 
replace the absent or disqualified member, the member or members thereof present
at any meeting and not disqualified from voting, whether or not he or they 
constitute a quorum, may unanimously appoint another member of the Board of 
Directors to act at the meeting in the place of any absent or disqualified 
member.  Any committee, to the extent allowed by law and provided in the 
resolution establishing such committee, shall have and may exercise all the 
powers and authority of the Board of Directors in the management of the business
and affairs of the Corporation.  Unless the Board of Directors or such committee
shall otherwise provide, regular and special meetings and other actions of any 
shall be governed by the provisions of this Article III applicable to meetings 
and actions of the Board of Directors.  Each committee shall keep regular 
minutes and report to the Board of Directors when required.

        Section 10.  Fees and Compensation.  Directors and members of committees
        ----------   ---------------------
may receive such compensation, if any, for their services, and such
reimbursement for expenses, as may be fixed or determined by the Board of
Directors. No such payment shall preclude any director from serving the
Corporation in any other capacity and receiving compensation therefor.

        Section 11.  Interested Directors.  No contract or transaction between 
        ----------   --------------------
the Corporation and one or more of its directors or officers, or between the
Corporation and any other corporation, partnership, association, or other
organization in which one or more of its directors or officers are directors or
officers, or have a financial interest, shall be void or voidable solely for
this reason, or solely because the director or officer is present at or
participates in the meeting of the Board of Directors or committee thereof which
authorizes the contract or transaction, or solely because his or their votes are
counted for such purpose if (a) the material facts as to his or their
relationship or interest and as to the contract or transaction are disclosed or
are known to the Board of Directors or the committee, and the Board of Directors
or committee in good faith authorizes the contract or transaction by the
affirmative votes of a majority of the disinterested directors, even though the
disinterested directors be less that a quorum; or (b) the material facts as to
his or their relationship or inter-

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<PAGE>
 
est and as to the contract or transaction are disclosed or are known to the 
stockholders entitled to vote thereon, and the contract or transaction is 
specifically approved in good faith by vote of the stockholders; or (c) the 
contract or transaction is fair as to the Corporation as of the time it is 
authorized, approved or ratified, by the Board of Directors, a committee thereof
or the stockholders.  Common or interested directors may be counted in 
determining the presence of a quorum at a meeting of the Board of Directors or 
of a committee which authorizes the contract or transaction.


                                  ARTICLE IV

                                   OFFICERS
                                   --------

        Section 1.  General.  The officers of the Corporation shall be chosen by
        ---------   -------
the Board of Directors and shall be a President, one or more Vice Presidents, a
Secretary and a Treasurer. The Board of Directors, in its discretion, may also
choose a Chairman of the Board of Directors (who must be a director) and
Assistant Secretaries, Assistant Treasurers and other officers. Such officers as
the Board of Directors may choose shall perform such duties and have such powers
as from time to time may be assigned to them by the Board of Directors. The
Board of Directors may delegate to any other officer of the Corporation the
power to choose such other officers and to prescribe their respective duties and
powers. Any number of offices may be held by the same person, unless otherwise
prohibited by law, the Certificate of Incorporation or these By-laws. The
officers of the Corporation need not be stockholders of the Corporation nor,
except in the case of the Chairman of the Board of Directors, need such officers
be directors of the Corporation.

        Section 2.  Election.  The Board of Directors at its first meeting held 
        ---------   --------
after each Annual Meeting of Stockholders shall elect the officers of the 
Corporation, who shall be subject to the control of the Board of Directors and 
shall hold their offices for such terms and shall exercise such powers and 
perform such duties as shall be determined from time to time by the Board of 
Directors, and all officers of the Corporation shall hold office until their 
successors are chosen and qualified,


                                       9
<PAGE>
 
or until their earlier resignation or removal.  Any officer elected by the Board
of Directors may be removed at any time by the Board of Directors with or 
without cause.  Any vacancy occurring in any office of the Corporation shall be 
filled by the Board of Directors.  The salaries of all officers of the 
Corporation shall be fixed by the Board of Directors.

        Section 3.  Voting Securities Owned by the Corporation.  Powers of 
        ---------   ------------------------------------------
attorney, proxies, waivers of notice of meeting, consents and other instruments
relating to securities owned by the Corporation may be executed in the name of
and on behalf of the Corporation by the President or any Vice President and any
such officer may, in the name of and on behalf of the Corporation, take all such
action as any such officer may deem advisable to vote in person or by proxy at
any meeting of security holders of any corporation in which the Corporation may
own securities and at any such meeting shall possess and may exercise any and
all rights and power incident to the ownership of such securities and which, as
the owner thereof, the Corporation might have exercised and possessed if
present. The Board of Directors may, by resolution, from time to time confer
like powers upon any other person or persons.


                                   ARTICLE V

                                     STOCK
                                     -----

        Section 1.  Form of Certificates.  Every holder of stock in the 
        ---------   --------------------
Corporation shall be entitled to have a certificate signed, in the name of the 
Corporation (a) by the Chairman of the Board of Directors, the President or a 
Vice President and (b) by the Treasurer or an Assistant Treasurer, or the 
Secretary or an Assistant Secretary of the Corporation, certifying the number of
shares owned by him in the Corporation.

        Section 2.  Signatures.  Where a certificate is countersigned by (a) a 
        ---------   ----------
transfer agent other than the Corporation or its employee or (b) a registrar
other than the Corporation or its employee, any other signature on the
certificate may be a facsimile. In case any officer, transfer agent or registrar
who has signed or whose facsimile signature has been placed upon a certificate
shall


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<PAGE>
 
have ceased to be such officer, transfer agent or registrar before such 
certificate is issued, it may be issued by the Corporation with the same effect 
as if he were such officer, transfer agent or registrar at the date of issue.

          Section 3.  Lost Certificates.  The Board of Directors may direct a 
          ---------   -----------------
new certificate to be issued in place of any certificate theretofore issued by
the Corporation alleged to have been lost, stolen or destroyed, upon the making
of an affidavit of that fact by the person claiming the certificate of stock to
be lost, stolen or destroyed. When authorizing such issue of a new certificate,
the Board of Directors may, in its discretion and as a condition precedent to
the issuance thereof, require the owner of such lost, stolen or destroyed
certificate, or his legal representative, to advertise the same in such manner
as the Board of Directors shall require and/or to give the Corporation a bond in
such sum as it may direct as indemnity against any claim that may be made
against the Corporation with respect to the certificate alleged to have been
lost, stolen or destroyed.

          Section 4.  Transfers.  Stock of the Corporation shall be 
          ---------   ---------
transferrable in the manner prescribed by law and in these By-laws. Transfers of
stock shall be made on the books of the Corporation only by the person named in
the certificate or by his attorney lawfully constituted in writing and upon the
surrender of the certificate therefor, which shall be cancelled before a new
certificate shall be issued.

          Section 5.  Record Date.  In order that the Corporation may determine 
          ---------   -----------
the stockholders entitled to notice of or to vote at any meeting of stockholders
or any adjournment thereof, or entitled to receive payment of any dividend or 
other distribution or allotment of any rights, or entitled to exercise any 
rights in respect of any change, conversion or exchange of stock or for the 
purpose of any other lawful action, the Board of Directors may fix, in advance, 
a record date, which shall not be more than sixty days nor less than ten days 
before the date of such meeting, nor more than sixty days prior to any other 
action.  A determination of stockholders of record entitled to notice of or to 
vote at a meeting of stockholders shall apply to any adjournment of the meet-

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<PAGE> 
ing; provided, however, that the Board of Directors may fix a new record date 
for the adjourned meeting. 

        Section 6.  Beneficial Owners.  The Corporation shall be entitled to 
        ---------   -----------------
recognize the exclusive right of a person registered on its books as the owner 
of shares to receive dividends, and to vote as such owner, and to hold liable 
for calls and assessments a person registered on its books as the owner of 
shares, and shall not be bound to recognize any equitable or other claim to or 
interest in such share or shares on the part of any other person, whether or not
it shall have express or other notice thereof, except as otherwise provided by 
law.

                                  ARTICLE VI

                                    NOTICES
                                    -------
        
        Section 1.  Notices.  Whenever written notice is required by law, the
        ---------   -------
Certificate of Incorporation or these By-laws, to be given to any director or 
stockholder, such notice may be given by mail, addressed to such director or 
stockholder, at his address as it appears on the records of the Corporation, 
with postage thereon prepaid, and such notice shall be deemed to be given at the
time when the same shall be deposited in the United States mail.  Written notice
may also be given personally or by telegram, telex, cable or facsimile 
transmission.

        Section 2.  Waivers of Notice.  Whenever any notice is required by law, 
        ---------   ----------------- 
the Certificate of Incorporation or these By-laws, to be given to any director 
or stockholder, a waiver thereof in writing, signed, by the person or persons 
entitled to said notice, whether before or after the time stated therein, shall 
be deemed equivalent thereto.

                                  ARTICLE VII

                              GENERAL PROVISIONS
                              ------------------

        Section 1.  Dividends.  Dividends upon the capital stock of the 
        ---------   ---------
Corporation, subject to the provisions of the Certificate of Incorporation, if 
any, may be declared by the Board of Directors at any regular or 

                                      12
<PAGE>
 
special meeting pursuant to law. Dividends may be paid in cash, in property or 
in shares of capital stock. Before payment of any dividend, there may be set 
aside out of any funds of the Corporation available for dividends such sum or 
sums as the Board of Directors from time to time, in its absolute discretion, 
deems proper as a reserve or reserves to meet contingencies, or for equalizing 
dividends, or for repairing or maintaining any property of the Corporation, or 
for any proper purpose, and the Board of Directors may modify or abolish any 
such reserve.

     Section 2. Disbursements. All checks or demands for money and notes of the 
     ---------  -------------
Corporation shall be signed by such officer or officers or such other person or 
persons as the Board of Directors may from time to time designate.

     Section 3. Fiscal Year. The fiscal year of the Corporation shall be fixed 
     ---------  -----------
by resolution of the Board of Directors.

     Section 4. Corporate Seal. The corporate seal shall have inscribed thereon 
     ---------  --------------
the name of the Corporation, the year of its organization and the words 
"Corporate Seal, Delaware". The seal may be used by causing it or a facsimile 
thereof to be impressed or affixed or reproduced or otherwise.

                                 ARTICLE VIII

                                INDEMNIFICATION
                                ---------------

     The Corporation shall indemnify to the full extent authorized or permitted 
by law (as now or hereafter in effect) any person made, or threatened to be 
made, a defendant or witness to any action, suit or proceeding (whether civil or
criminal or otherwise) by reason of the fact that he, his testator or intestate,
is or was a director or officer of the Corporation or by reason of the fact that
such director or officer, at the request of the Corporation, is or was serving
any other corporation, partnership, joint venture, trust, employee benefit plan
or other enterprise, in any capacity.

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<PAGE>
 
                                  ARTICLE IX

                                  AMENDMENTS
                                  ----------

     These By-laws may be altered, amended or repealed, in whole or in part, or 
new By-laws may be adopted by either the affirmative vote of the holders of 
sixty-six and two-thirds percent (66-2/3%) of the outstanding capital stock of 
the Corporation entitled to vote thereon or by the Board of Directors.


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