Exhibit 10.4

THIRD AMENDMENT TO SHAREHOLDERS
AGREEMENT OF DISCOVERY COMMUNICATIONS, INC.

        THIRD AMENDMENT TO SHAREHOLDERS AGREEMENT, dated as of September , 2001 (the "Third Amendment"), by and among Discovery Communications, Inc., a Delaware close corporation (the "Company"), Cox Communications Holdings, Inc., a Delaware corporation (as successor in interest to Cox Discovery, Inc., "Cox"), Advance/Newhouse Programming Partnership, a New York general partnership (as successor in interest to Newhouse Broadcasting Corporation, "Newhouse"), LMC Discovery, Inc., a Colorado corporation (formerly known as TCI Cable Education, Inc., "LMC"), John S. Hendricks ("Hendricks"; and together with Cox, LMC and Newhouse, the "Existing Stockholders"), and Advance Programming Holdings Corp., a New York corporation ("Advance", and together with the Existing Stockholders, collectively the "Stockholders" and each individually as a "Stockholder").

RECITALS

        A.    The Existing Stockholders are parties to that certain Shareholders Agreement, dated as of November 30, 1991, of the Company (as the same has been and shall be amended from time to time, the "Shareholders Agreement"). Unless otherwise defined herein, capitalized terms used herein which are defined in the Shareholders Agreement shall have the same meanings when used herein as therein defined.

        B.    The Company has offered for sale that certain Class B Non-voting common stock, $0.01 par value (the "Class B Stock") to each of the Existing Stockholders, pro rata, based on the equity held thereby in the Company. Newhouse has requested that in lieu of Newhouse, Advance be permitted to acquire the pro rata portion of the Class B Stock that Newhouse would otherwise be entitled to acquire (the "Newhouse Portion"). In connection therewith, and as a precondition thereto, Advance shall be admitted as a party to the Shareholders Agreement. The Existing Stockholders, which constitute the holders of all of the issued and outstanding equity of the Company, have agreed that Advance may acquire the Newhouse Portion and be admitted as a party to the Shareholders Agreement.

        C.    In accordance with Section 10.03 of the Shareholders Agreement, the parties hereto desire to evidence the agreement of each of the Existing Stockholders to the acquisition by Advance of the Newhouse Portion, to amend the Shareholders Agreement to provide for the addition of Advance as a party thereto and to otherwise reflect the issuance of the Class B Stock.

        NOW, THEREFORE, the parties, intending to be legally bound, hereby agree as follows:

        1.     By execution and delivery of this Third Amendment thereby, each of the Existing Stockholders hereby consents to the acquisition by Advance of the Newhouse Portion.

        2.     By execution and delivery of this Third Amendment, Advance is hereby admitted as a party to the Shareholders Agreement and Advance agrees to be bound by and subject to the terms and provisions thereof.

        3.     The definitions of "Stockholder" and "Stockholders" as set forth in the preamble of the Shareholders Agreement are hereby amended to include Advance as a "Stockholder".

        4.     Article I of the Shareholders Agreement is hereby amended to delete the definition of "Capital Stock" therefrom, to insert the following definition of "Capital Stock" in lieu thereof, and include the following additional definitions therein:

        "Advance" shall mean Advance Programming Holdings Corp., a New York corporation.

        "Capital Stock" shall mean the Class A Stock and the Class B Stock.

        "Class A Stock" shall mean the Class A Common Stock, par value $0.01 per share, of the Company.

        "Class B Stock" shall mean the Class B Non-voting Common Stock, par value $0.01 per share, of the Company."

        5.     Article II of the Shareholders Agreement is hereby amended by deleting Section 2.02 therefrom and inserting the following Section 2.02 in lieu thereof:

        "2.02 Voting Rights.

a.

Each Stockholder shall be entitled to one (1) vote (or fraction thereof) for each share of Class A Stock (or fraction thereof) owned by such Stockholder.



b.

Each Stockholder shall not be entitled to any vote for any share of Class B Stock (or fraction thereof) owned by such Stockholder, except as may otherwise be required by the laws of the State of Delaware."

        6.     Schedule I to the Shareholders Agreement is herby deleted from therefrom and Schedule I attached hereto is hereby inserted in lieu thereof.

        7.     This Third Amendment shall become effective immediately upon the execution of this Third Amendment by all parties hereto.

        8.     Except as expressly amended hereby, the Shareholders Agreement shall remain in full force and effect in accordance with its terms.

        9.     This Third Amendment may be executed in counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

        IN WITNESS WHEREOF, the parties herein have executed this Third Amendment as of the date first set forth above.

/s/ DISCOVERY COMMUNICATIONS, INC.

/s/ COX COMMUNICATIONS HOLDINGS, INC.

/s/ ADVANCE/NEWHOUSE PROGRAMMING PARTNERSHIP

By: ADVANCE PROGRAMMING HOLDINGS CORP.
A General Partner

/s/ LMC DISCOVERY, INC.

/s/ JOHN S. HENDRICKS

/s/ ADVANCE PROGRAMMING HOLDINGS CORP.

Schedule I

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