Exhibit (d)(4)

CONFIDENTIAL

UNDERTAKING TO TENDER SHARES TO AN OFFER TO BE MADE BY IBM FOR ILOG

THIS UNDERTAKING IS ENTERED INTO BETWEEN:

1. INRIA-Transfert, a French corporation (société anonyme), having a share capital of 13,186,840 euros, whose registered office is located at Rocquencourt, domaine de Voluceau, 78153 Le Chesnay and who is registered with the Versailles under number 418 339 230, represented by its General Director Mr. Laurent KOTT, duly authorised for the purposes hereof,

(hereinafter the “Shareholder”)

and

2. International Business Machines Corporation, whose registered office is located at New Orchard Road Armonk, New York, 10504, represented by Archie Colburn (GLN), duly authorised for the purposes hereof, or any of its subsidiaries it determines to substitute for it for the purposes of the present document,

(hereinafter the “Offeror”).

IT IS HEREBY AGREED AS FOLLOWS:

1. UNDERTAKING TO TENDER

1.1 Subject to and in consideration of the Offeror making a public cash offer in France and the United States for all of the shares listed on Eurolist, and other securities giving access to the shares, of Ilog (the “Company”) at a price of euros 10 per share, in accordance with applicable laws and regulations in France and the United States and subject to the conditions set out in Annex 1 hereto (the “Offer”), Shareholder hereby undertakes, provided that the Offer is filed with the Autorité des Marchés Financiers (the “AMF”) not later than 15 September 2008 (or such later date as may be agreed between the Offeror and the Company), subject to the approval of the board of directors of INRIA (Institut National de Recherche en Informatique et en Automatique), a French Etablissement Public à caractère Scientifique et Technologique governed by Decree n°85-831 of 2 August 1985, whose registered office is located at Domaine de Voluceau — Rocquencourt B.P. 105 78 153 Le Chesnay Cedex, and subject to the provisions of clause 2.1 below, that:

(i) being the beneficial and registered holder of 1,237,750 ordinary shares in the capital of the Company (the “Shares”) and having all relevant authority to, and, until the Shares are transferred to the Offeror, continuing to have all relevant authority to, accept the Offer in respect of the Shares, it shall, within five (5) trading days of the opening of the Offer, tender to the Offer all of the Shares by giving irrevocable instructions to the institution holding its share account to tender the Shares to the Offer immediately, and shall promptly complete, execute and deliver all other documents and take any other action which the Offeror may reasonably require to complete the transfer of the Shares to the Offeror;

(ii) it shall not, prior to the closing or lapsing of the Offer or the withdrawal of the Offer (whichever is the earlier), sell, transfer, charge, pledge, encumber, grant any option over or otherwise dispose of or permit the sale, transfer, charging, encumbering, granting of any option over or other disposition of (save to the Offeror under the Offer), or accept any other offer in respect of, all or any of the Shares or enter into any agreement or

arrangement with any other person, whether conditionally or unconditionally, to do all or any of the acts referred to in this paragraph;

(iii) the Shares shall be acquired pursuant to the Offer free from all liens, charges and encumbrances and together with all rights attached thereto including all rights to dividends or other distributions hereafter declared, paid or made;

(iv) it shall not (in its capacity as a shareholder or otherwise) take any step to impede, prevent or delay the Offer becoming successful;

(v) it shall permit public disclosure by the Offeror, including in a press release, in the tender offer notice relating to the Offer and as may be disclosed to the Workers’ Council of the Company, of the contents of this Agreement, including, but not limited to, the contents and commitments contained in this Section 1;

(vi) it shall confirm to any other beneficial owner of Shares, upon inquiry of such other beneficial owner, that it has made the commitment contained in this Section 1; and

(vii) it shall not, prior to the closing or lapsing of the Offer or the withdrawal of the Offer (whichever is the earlier), solicit nor encourage any general offer for the issued share capital of the Company from any third party and shall immediately inform the Offeror of any approach by a third party which may lead to such an offer.

1.2 The expression the “Shares” shall include any other ordinary shares in the Company attributable to or derived from the Shares and any other ordinary shares in the Company of which the Shareholder becomes the holder after the date hereof and is able to tender to the Offer.

2. THIRD PARTY OFFER

2.1 Shareholder’s undertakings pursuant to clause 1 above shall be void in the event that a third party (the “Third Party”) files: (i) a public offer prior to the filing of the Offer with the AMF, or (ii) after the filing with the AMF and opening of the Offer, a public offer competing with or higher than that of the Offeror, and in each case the relevant offer (the “Third Party Offer”) is declared compliant (“conforme”) by the AMF, provided however that all of Shareholder’s undertakings under clause 1 above will immediately apply with full force, mutatis mutandis, in the event that Offeror makes a competing offer or a higher bid, as the case may be, that is declared compliant by the AMF, in which case Shareholder shall observe such undertakings, and tender the Shares to such offer by the Offeror, as if the undertakings of Shareholder had never been void.

3. MISCELLANEOUS

3.1 This Agreement is entered into for a term expiring on 30 June 2009.

3.2 This Agreement shall be governed by and interpreted in accordance with French law and is entered into intuitu personae and may be neither assigned nor transferred.

3.3 The parties hereby agree that all disputes that may arise in respect of the validity, interpretation or performance of this Agreement shall be referred to the exclusive jurisdiction of the Commercial Court of Paris.

Made in Paris, on 25 July 2008 in two (2) originals by:

INRIA-TRANSFERT	INTERNATIONAL BUSINESS MACHINES CORPORATION

	Entered into in Armonk, NY on 27 July 2008 /s/ Archie Colburn

/s/ Laurent Kott		/s/ Archie Colburn
By: Laurent Kott	By: Archie Colburn

General Director	Authorized Signor

ANNEX 1

KEY TERMS AND CONDITIONS OF THE FRENCH OFFER AND THE U.S. OFFER

Maximum number of shares to be purchased in the French Offer and the U.S. Offer (either directly or through ADS)		23,109,853 Shares (including 19,208,248 issued Shares + 3,647,005 Shares to be issued upon exercise of Stock Options + 254,000 Shares to be issued upon exercise of Warrants)

Maximum number of Warrants to be purchased in the French Offer and the U.S. Offer		254,000 Warrants

Price per Share		EUR 10.00 (with all rights attached, including any annual dividend for the year end 2008)

Minimum tender condition

Bidder will only proceed with the Offers if at the date of the closing of the French Offer, the Bidder is entitled to hold Shares representing, at the date of the closing of the French Offer, at least 66.67% of the share capital and voting rights of Target on a fully-diluted basis.

For the purposes of the calculation of this 66.67% threshold, the following will be taken into consideration:

· as numerator, the sum of (i) Treasury Shares not required to satisfy, before the closing of the French Offer, rights under stock option plans, free Share allotment plans, or the liquidity agreement which ZION entered into with Oddo Corporate Finance, and (ii) the total number of Shares validly tendered to the French Offer and the US Offer (including the Shares represented by ADSs) and the total number of Shares to be issued upon exercise of the Warrants validly tendered to the French Offer, as of the date of the closing of the French Offer and prior to its reopening; and

· as denominator, the sum of (i) the total number of outstanding Shares on the date of the closing of the French Offer, including the Shares represented by ADSs and Treasury Shares and (ii) the maximum number of Shares to be issued upon the exercise of all Stock Options and Warrants, whether or not exercisable, as of the date of the closing of the French Offer and prior to its reopening.

Antitrust condition to closing of the Offers

Closing of the Offers shall be subject to:

(i) the authorisation of the competent US anti-trust authorities or the expiration or termination of the waiting period under the Hart-Scott-Rodino Antitrust Improvements Act of 1976, as amended; and to

(ii) the authorisation of the European Commission under Article 6(1)(b) of the European Union Council Regulation (EEC) No. 1 39/2004.