Filing Details

CUSIP No. 918905 10 0

CUSIP No.  918905 10 0

CUSIP No.  918905 10 0

CUSIP No.  918905 10 0

CUSIP No.  918905 10 0

AMENDMENT NO. 76

TO SCHEDULE 13D

Capitalized terms not otherwise defined in this Amendment No. 76 to this Statement on Schedule 13D (this "Statement") shall have the meanings assigned to such terms in Amendment No. 73 to this Statement.  This Statement relates to the common stock, par value $0.01 per share (the "Shares"), of Valhi, Inc., a Delaware corporation ("Valhi").  Items 2, 4, 5 and 6 of this Statement are hereby amended as set forth below.  The Reporting Persons (as defined below) are filing this amendment as a result of certain transfers of Shares by VHC (as defined below) in payment for redemption of preferred stock of VHC.

Item 2.

Identity and Background.

The following is a description of the relationships among the Reporting Persons.

All of Contran's outstanding voting stock is held by a family trust (the "Family Trust") established for the benefit of Ms. Simmons and Ms. Connelly and their children, for which Ms. Simmons and Ms. Connelly are co-trustees, or is held directly by Ms. Simmons and Ms. Connelly or entities related to them.  Ms. Simmons and Ms. Connelly are sisters.

Ms. Simmons and Ms. Connelly also serve as co-chairs of the Contran Board, and one other member of Contran management also serves on the Contran Board.  As co-trustees of the Family Trust, Ms. Simmons and Ms. Connelly has the shared power to vote and direct the disposition of the shares of Contran stock held by the Family Trust, and Ms. Simmons and Ms. Connelly each have the power to vote and direct the disposition of shares of Contran stock they hold directly or which is held by other entities related to them.

Contran is the holder of 100% of the outstanding common stock of Dixie Rice and may be deemed to control Dixie Rice.  Dixie Rice is the direct holder of 100% of the outstanding common stock of VHC and may be deemed to control VHC.

Ms. Simmons and Ms. Connelly (or a trust for which Ms. Connelly is the sole trustee and sole beneficiary, whose Shares are combined with those held directly by Ms. Connelly for purposes of the percentage below) directly hold, or are related to the following persons or entities that directly hold, the following percentages of the 339,170,949 Shares outstanding as of the close of business on May 15, 2018 based on information from Valhi (the "Outstanding Shares"):

VHC may be deemed to control Valhi.  Contran may be deemed to control VHC, by virtue of its ownership of Dixie Rice shares.

Ms. Simmons and Ms. Connelly directly hold, or are related to the following persons or entities that directly hold, the following percentages of the outstanding shares of Kronos Worldwide common stock:

Together, Valhi, NL Industries, Inc. ("NL") (and its wholly-owned subsidiary NLKW) and Contran may be deemed to control Kronos Worldwide.

Ms. Simmons and Ms. Connelly directly hold, or are related to the following persons or entities that directly hold, the following percentages of the outstanding shares of NL common stock:

Together, Valhi and Kronos Worldwide may be deemed to control NL.

NL (including a wholly owned subsidiary of NL) and Kronos Worldwide own 14,372,970 Shares and 1,724,916 Shares, respectively.  As already stated, Valhi is the direct holder of approximately 82.9% of the outstanding shares of common stock of NL and 50.0% of the outstanding shares of Kronos Worldwide common stock.  As a result of Valhi's direct and indirect ownership of NL and Kronos Worldwide and pursuant to Delaware law and Section 13(d)(4) of the Exchange Act, Valhi treats the Shares that NL and Kronos Worldwide own as treasury stock for voting purposes.  For the purposes of this statement, such Shares that NL and Kronos Worldwide hold are not deemed outstanding.

By virtue of the stock ownership of each of Kronos Worldwide, NL, Valhi, VHC, Dixie Rice and Contran, the role of Ms. Simmons and Ms. Connelly as co-trustees of the Family Trust, Ms. Simmons and Ms. Connelly being beneficiaries of the Family Trust, the direct holdings of Contran voting stock by each of Ms. Simmons, Ms. Connelly and entities related to them, the positions as co-chairs of the Contran Board by each of Ms. Simmons and Ms. Connelly, in each case as described above, (a) Ms. Simmons and Ms. Connelly may be deemed to control the Family Trust, Contran, Dixie Rice, VHC, Valhi, NL and Kronos Worldwide and (b) Ms. Simmons and Ms. Connelly, Contran, Dixie Rice, VHC, Valhi, NL and Kronos Worldwide may be deemed to possess indirect beneficial ownership of, and a pecuniary interest in, shares of common stock directly held by such entities, including any Shares.  However, Ms. Simmons and Ms. Connelly each disclaims beneficial ownership of, and such pecuniary interest in, such shares beneficially owned, directly or indirectly, by any of such entities, except to the extent of their direct beneficial ownership in shares of such entities.

The Reporting Persons understand, based on ownership filings with the SEC or upon information provided by the persons listed on Schedule B to this Statement, that such persons may be deemed to own beneficially the Shares as indicated on Schedule C to this Statement.

Item 4.

Purpose of Transaction

Item 4 is amended and supplemented as follows.

Depending upon their evaluation of Valhi's business and prospects, and upon future developments (including, but not limited to, performance of the Shares in the market, availability of funds, alternative uses of funds, and money, stock market and general economic conditions), any of the Reporting Persons or other entities that may be deemed to be related to Contran may from time to time purchase Shares, and any of the Reporting Persons or other entities that may be deemed to be related to Contran may from time to time dispose of all or a portion of the Shares held by such person, or cease buying or selling Shares.  Any such additional purchases or sales of Shares may be in open market or privately negotiated transactions or otherwise.

The information included in Item 2 of this Statement is hereby incorporated herein by reference.  As described under Item 2 of this Statement, Ms. Simmons and Ms. Connelly may be deemed to control Valhi.

Except as described in this Item 4, none of the Reporting Persons nor, to the best knowledge of such persons, any other person named in Schedule B to this Statement has formulated any plans or proposals which relate to or would result in any matter required to be disclosed in response to paragraphs (a) through (j) of Item 4 of Schedule 13D.

Item 5.

Interest in Securities of the Issuer.

Item 5 is amended and supplemented as follows.

By virtue of the relationships described under Item 2 of this Statement:

Except for 56,136 Shares (the "Connelly Shares") she holds directly or through a trust for which she is sole trustee and sole beneficiary, Ms. Connelly disclaims beneficial ownership of all Shares.  Ms. Lisa Simmons disclaims beneficial ownership of all Shares.

Item 6.

Contracts, Arrangements, Understandings or Relationships with Respect to Securities of the Issuer.

Item 6 is amended and supplemented as follows.

The information included in Items 2, 4 and 5 of this Statement is hereby incorporated herein by reference.

To the best of their knowledge, none of the Reporting Persons or any person named in Schedule B to this Statement has any contract, arrangement, understanding or relationship (legal or otherwise) with any person with respect to Shares, including, but not limited to, transfer or voting of any such securities, finder's fees, joint ventures, loans or option arrangements, puts or calls, guarantees of profits, division of profits or losses, or the giving or withholding of proxies.

Signature

After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this Statement is true, complete and correct.

Date: May 17, 2018

Serena Simmons Connelly, Signing in the capacities listed on Schedule "A" attached hereto and incorporated herein by reference.

Signature

After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this Statement is true, complete and correct.

Date: May 17, 2018

Lisa K. Simmons

Signing in the capacities listed on Schedule "A" attached hereto and incorporated herein by reference.

Signature

After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this Statement is true, complete and correct.

Date: May 17, 2018

Robert D. Graham, Signing in the capacities listed on Schedule "A" attached hereto and incorporated herein by reference.

SCHEDULE A

LISA K. SIMMONS, as CO-TRUSTEE of the Family Trust and as CO-CHAIR of the Contran Board.

SERENA SIMMONS CONNELLY, as CO-TRUSTEE of the Family Trust, as CO-CHAIR of the Contran Board, and as holder (directly or indirectly) of the Connelly Shares.

ROBERT D. GRAHAM, as PRESIDENT and CHIEF EXECUTIVE OFFICER of Contran and CHAIRMAN OF THE BOARD, PRESIDENT and CHIEF EXECUTIVE OFFICER of each of:

DIXIE RICE AGRICULTURAL L.L.C.

VALHI HOLDING COMPANY

SCHEDULE B

The names of the directors and executive officers of the Reporting Persons and their present principal occupations are set forth below.  Each such person is a citizen of the United States of America and the business address of each such person is 5430 LBJ Freeway, Suite 1700, Dallas, Texas  75240.

SCHEDULE C

Based upon ownership filings with the Commission or upon information provided by the persons listed on Schedule B to this Statement, such persons may be deemed to personally beneficially own Shares, as outlined below:

(1)

Does not include other Shares of which Ms. Connelly may be deemed to possess indirect beneficial ownership as described in Items 2 and 5(a) of this Statement.  Except for the 56,136 Shares she holds directly or through a trust for which she is sole trustee and sole beneficiary, Ms. Connelly disclaims beneficial ownership of all Shares.

(2)	Does not include Shares of which Ms. Lisa Simmons may be deemed to possess indirect beneficial ownership as described in Items 2 and 5(a) of this Statement.  Ms. Lisa Simmons disclaims beneficial ownership of all Shares.