EXHIBIT 4.13 REDEMPTION AGREEMENT This Redemption Agreement (this "Agreement") is made by and between NL Industries, Inc., a New Jersey corporation ("NL"), and Kronos International, Inc., a Delaware corporation ("KII"), as of June 6, 2002. RECITALS A. NL is a party to an Indenture dated as of October 20, 1993, with JPMorgan Chase Bank, formerly known as Chemical Bank, as Trustee thereunder (the "Senior Indenture") with respect to NL's 11 3/4% Senior Secured Notes Due 2003 (the "Senior Notes"). B. In connection with the Senior Indenture, KII issued its Second-Tier Senior Mirror Note (the "Mirror Note") to its direct parent, Kronos, Inc. ("KI"), which Mirror Note KI pledged to NL to secure KI's First-Tier Senior Mirror Note and NL in turn pledged to the Trustee to secure NL's obligations under the Senior Indenture. C. KII intends to make a private placement of certain Euro-based bonds to raise funds for debt reduction, including satisfaction of the Mirror Note (the "Debt Offering"). D. KII is willing to loan or otherwise transfer to NL sufficient proceeds of the Debt Offering in order to redeem the outstanding Senior Notes (including all accrued interest issued by NL pursuant to the Senior Indenture the redemption and discharge of the NL Debt (the "Redemption"), upon which discharge the Mirror Note will be deemed satisfied in full. E. NL is willing to provide notice on or before June 10, 2002 to the Trustee under the Senior Indenture of NL's intent to effect such redemption, and instructions to the Trustee to issue notice of redemption to the Holders of the Senior Notes, upon receipt of such proceeds from the Debt Offering and to provide to the Trustee all other certificates, agreements, instruments and documents contemplated by the Senior Indenture or reasonably requested by the Trustee in connection with such redemption. F. NL and KII wish to enter into this agreement to facilitate the consummation of the Debt Offering and related transactions, the redemption of the Senior Notes and the other transactions more specifically described in this Agreement. AGREEMENTS 1. On or before June 12, 2002, NL agrees to provide notice to the Trustee under the Senior Indenture of NL's intent to effect the Redemption, and irrevocable instructions to the Trustee to issue notice of redemption to the Holders of the Senior Notes, upon receipt of sufficient proceeds of the Debt Offering in order to effect the Redemption (the "Redemption Amount"). NL agrees to timely deliver to the Trustee all other certificates, agreements, instruments and documents contemplated by the Senior Indenture or reasonably requested by the Trustee in connection with the Redemption in order to allow the notice of Redemption to be issued by the Trustee on June 26, 2002 or such other date on which the Redemption Amount has been deposited with the Trustee. 2. As soon as reasonably practical after consummation of the Debt Offering, KII agrees to loan or otherwise transfer to NL, in a mutually acceptable form of transaction (the "Transfer Transaction"), the Redemption Amount. The Redemption Amount will be transferred directly to a Trustee trust account. Pending redemption of the Senior Notes, the Trustee will be authorized to invest the Redemption Amount in short term United States Treasury securities or money market funds which invest only in United States Treasury securities with a dollar weighted average maturity of ninety (90) days or less and that seek to maintain a one dollar per share net asset value. After redemption of the Senior Notes, any amounts remaining in the deposit account will be returned to KII. 3. Upon consummation of the Redemption, NL and KII acknowledge that the Mirror Note will be deemed satisfied in full and, unless expressly agreed otherwise in writing in connection with the Transfer Transaction, NL shall be deemed to have satisfied all obligations to KII with respect to the Transfer Transaction, including without limitation any loan by KII to NL of the Redemption Amount. Upon release of the pledge of the Mirror Note by the Trustee, NL agrees to deliver, or cause KI to deliver, to KII the original of the Mirror Note for cancellation by KII. 4. NL and KII each agree to execute all documents and take any and all other actions that the parties deem to be necessary or desirable to consummate the transactions contemplated by this Agreement. 5. This Agreement will be governed by and construed in accordance with the laws of the State of Delaware, without regard to its conflicts of laws rules. 6. This Agreement will be binding upon, and will inure to the benefit of, NL and KII and their respective successors and assigns. 7. This Agreement may not be altered, amended, changed, terminated or modified, or compliance with any provision waived, in any respect or any particular, except by written instrument executed by each of NL and KII. 8. This Agreement may be executed in any number of counterparts, each of which will be deemed an original but all of which will constitute one and the same instrument. 2 Each of the undersigned has executed this Redemption Agreement as of the date first written above regardless of the actual date of signing. NL INDUSTRIES, INC. By: /s/ Robert D. Hardy ---------------------------------------------- Name: Robert D. Hardy -------------------------------------------- Title: Vice President ------------------------------------------- KRONOS INTERNATIONAL, INC. By: /s/ Dr. Ulfert Fiand ---------------------------------------------- Name: Dr. Ulfert Fiand -------------------------------------------- Title: President, Manufacturing and Technology ------------------------------------------- By: /s/ Dr. Lawrence A. Wigdor ---------------------------------------------- Name: Dr. Lawrence A. Wigdor -------------------------------------------- Title: Chief Executive Officer ------------------------------------------- 3