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    <div style="text-align: center; font-family: 'Times New Roman', Times, serif; font-size: 10pt; font-weight: bold;">UNITED STATES</div>

    <div style="text-align: center; font-family: 'Times New Roman', Times, serif; font-size: 10pt; font-weight: bold;">SECURITIES AND EXCHANGE COMMISSION</div>

    <div style="text-align: center; font-family: 'Times New Roman', Times, serif; font-size: 10pt; font-weight: bold;">Washington, D.C.&#160;&#160; 20549</div>

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    <div style="text-align: center; font-family: 'Times New Roman', Times, serif; font-size: 12pt; font-weight: bold;">CURRENT REPORT</div>

    <div style="text-align: center; font-family: 'Times New Roman', Times, serif; font-size: 12pt; font-weight: bold;">Pursuant to Section 13 or 15(d) of The Securities Exchange Act of 1934</div>

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    <div style="text-align: center; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">Date of Report (Date of earliest event reported)</div>

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            <div style="text-align: center; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">(IRS Employer</div>
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            <div style="text-align: center; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">(Zip Code)</div>
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    <div style="text-align: center; margin-top: 12pt; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">Registrant&#8217;s telephone number, including area code</div>

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    <td style="width: 23.65%; vertical-align: top;">&#160;</td>

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            <div style="text-align: center; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">(Former name or former address, if changed since last report.)</div>
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    <td style="width: 23.66%; vertical-align: top;">&#160;</td>

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    <div style="text-align: justify; margin-top: 18pt; margin-bottom: 12pt; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">Check the appropriate box below if the Form 8-K filing is intended to simultaneously satisfy the filing obligation
      of the registrant under any of the following provisions (see General Instruction A.2):</div>

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    <td style="width: 93.13%; vertical-align: middle;">
            <div style="text-align: justify; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">Written communications pursuant to Rule 425 under the Securities Act (17 CFR 230.425)</div>
          </td>

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    <td style="width: 6.87%; vertical-align: top;">&#160;</td>

    <td style="width: 93.13%; vertical-align: middle;">&#160;</td>

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  <tr>

    <td style="width: 6.87%; vertical-align: top;">&#160;</td>

    <td style="width: 93.13%; vertical-align: middle;">&#160;</td>

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    <td style="width: 93.13%; vertical-align: middle;">
            <div style="text-align: justify; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">Pre-commencement communications pursuant to Rule 14d-2(b) under the Exchange Act (17 CFR 240.14d-2(b))</div>
          </td>

  </tr>

  <tr>

    <td style="width: 6.87%; vertical-align: top;">&#160;</td>

    <td style="width: 93.13%; vertical-align: middle;">&#160;</td>

  </tr>

  <tr>

    <td style="width: 6.87%; vertical-align: top;">
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    <td style="width: 93.13%; vertical-align: middle;">
            <div style="text-align: justify; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">Pre-commencement communications pursuant to Rule 13e-4(c) under the Exchange Act (17 CFR 240.13e-4(c))</div>
          </td>

  </tr>


</table>
    <div style="text-align: justify; margin-top: 12pt; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">Securities registered pursuant to Section 12(b) of the Act:</div>

    <div><br />
    </div>

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    <td style="width: 37.99%; vertical-align: bottom; border-bottom: #000000 2px solid;">
            <div style="text-align: center; font-family: 'Times New Roman', Times, serif; font-size: 8pt; font-weight: bold;">Title of each class</div>
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    <td style="width: 15%; vertical-align: bottom; border-bottom: #000000 2px solid;">
            <div style="text-align: center; font-family: 'Times New Roman', Times, serif; font-size: 8pt; font-weight: bold;">Trading</div>
            <div style="text-align: center; font-family: 'Times New Roman', Times, serif; font-size: 8pt; font-weight: bold;">Symbol(s)</div>
          </td>

    <td style="width: 1%; vertical-align: bottom;">&#160;</td>

    <td style="width: 45%; vertical-align: bottom; border-bottom: #000000 2px solid;">
            <div style="text-align: center; font-family: 'Times New Roman', Times, serif; font-size: 8pt; font-weight: bold;">Name of each exchange on which registered</div>
          </td>

  </tr>

  <tr>

    <td style="width: 37.99%; vertical-align: top;">
            <div style="text-align: center; font-family: 'Times New Roman', Times, serif; font-size: 8pt;"><ix:nonNumeric name="dei:Security12bTitle" id="Fact_55dd72877e1443d3bf62943afd95ca57" contextRef="c20210526to20210526">Common stock</ix:nonNumeric><br />
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    <td style="width: 1%; vertical-align: bottom;">&#160;</td>

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    <td style="width: 1%; vertical-align: bottom;">&#160;</td>

    <td style="width: 45%; vertical-align: bottom;">
            <div style="text-align: center; font-family: 'Times New Roman', Times, serif; font-size: 8pt;"><ix:nonNumeric name="dei:SecurityExchangeName" id="Fact_4c37982aa7b0424ebb0175a071011324" contextRef="c20210526to20210526">NYSE</ix:nonNumeric><br />
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          </td>

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</table>
    <div>
      <div><br />
      </div>

      <div style="text-align: left; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">Indicate by check mark whether the registrant is an emerging growth company as defined in Rule 405 of the Securities Act of 1933 (17&#160;CFR &#167;230.405) or Rule
        12b-2 of the Securities Exchange Act of 1934 (17 CFR &#167;240.12b-2).</div>

    </div>

    <div>
      <div><br />
      </div>

      <div style="text-align: right; margin-top: 6pt; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">Emerging growth company&#160; <ix:nonNumeric name="dei:EntityEmergingGrowthCompany" id="Fact_269afe8429cd48dc8768ed2954d283c7" contextRef="c20210526to20210526" format="ixt-sec:boolballotbox">&#x2610;</ix:nonNumeric></div>

    </div>

    <div>
      <div><br />
      </div>

      <div style="text-align: left; margin-top: 6pt; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for complying
        with any new or revised financial accounting standards provided pursuant to Section&#160;13(a) of the Exchange Act.&#160;&#160;<span style="font-size: 10pt; font-family: 'Times New Roman', Times, serif;">&#9744;</span></div>

    </div>

    <div style="clear: both; margin-top: 10pt; margin-bottom: 10pt;">
      <div style="page-break-after:always;">
        <hr style="margin: 4px 0px; width: 100%; border-width: 0; height: 2px; color: #000000; background-color: #000000; clear: both;" /></div>

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  <tr>

    <td style="width: 72pt; vertical-align: top; align: right; font-family: 'Times New Roman', Times, serif; font-size: 10pt; font-weight: bold;">Item 5.02</td>

    <td style="width: auto; vertical-align: top; text-align: justify;">
            <div style="font-family: 'Times New Roman', Times, serif; font-size: 10pt; font-weight: bold;">Departure of Directors or Certain Officers; Election of Directors; Appointment of Certain Officers; Compensatory Arrangements of Certain Officers.</div>
          </td>

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</table>
    <div><br />
    </div>

    <div style="text-align: justify; text-indent: 36pt; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">On May 26, 2021, James W. Brown, executive vice president and chief financial officer of the registrant, provided notice to the
      registrant of his retirement, effective as of June 1, 2021, as chief financial officer of the registrant.&#160; In connection with his retirement as chief financial officer of the registrant, Mr. Brown also provided notice to Kronos Worldwide, Inc.
      (&#8220;Kronos Worldwide&#8221;), an affiliate of the registrant, of his retirement as chief financial officer of Kronos Worldwide as of June 1, 2021.&#160; Following such retirements, Mr. Brown continues to be employed by Contran Corporation (&#8220;Contran&#8221;), the
      privately-held parent corporation of the registrant, and to serve as executive vice president of the registrant, Kronos Worldwide and Contran.</div>

    <div><br />
    </div>

    <div style="text-align: left; text-indent: 36pt; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">Following such retirement notice of Mr. Brown, the registrant&#8217;s board of directors took action, also effective as of June 1, 2021, to:</div>

    <div><br />
    </div>

    <div>
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    <td style="width: 54pt; vertical-align: top; align: right;">
              <div style="text-align: left; margin-left: 36pt; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">&#8226;</div>
            </td>

    <td style="width: auto; vertical-align: top;">
              <div style="text-align: left; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">elect Amy Allbach Samford as senior vice president and chief financial officer of the registrant; and</div>
            </td>

  </tr>


</table>
    </div>

    <div>
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    <td style="width: 54pt; vertical-align: top; align: right;">
              <div style="text-align: left; margin-left: 36pt; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">&#8226;</div>
            </td>

    <td style="width: auto; vertical-align: top;">
              <div style="text-align: left; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">elect Patty S. Brinda as vice president and controller of the registrant.</div>
            </td>

  </tr>


</table>
    </div>

    <div><br />
    </div>

    <div style="text-align: left; text-indent: 36pt; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">Effective as of June 1, 2021, Michael S. Simmons, who formerly served as vice president and chief accounting officer of the registrant,
      became senior vice president, finance of the registrant, Kronos Worldwide and Contran and senior vice president and chief financial officer of CompX International Inc. (&#8220;CompX&#8221;), an affiliate of the registrant. Upon Ms. Brinda&#8217;s election, Mr. Simmons
      ceased serving as the registrant&#8217;s principal accounting officer.</div>

    <div><br />
    </div>

    <div style="text-align: left; text-indent: 36pt; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">Ms. Samford, age 47, has served as senior vice president and chief financial officer of the registrant since June 1, 2021.&#160; She previously
      served as the registrant&#8217;s vice president and controller from 2016 to June 2021.&#160; She currently serves as senior vice president and chief financial officer of Contran and the registrant&#8217;s affiliate NL Industries, Inc. (&#8220;NL&#8221;).&#160; Ms. Samford has served
      in various accounting and financial positions (including officer positions) in various companies related to us and Contran since 2006.&#160; Immediately prior to June 1, 2021, Ms. Samford served as vice president and chief financial officer of each of NL
      and CompX.</div>

    <div><br />
    </div>

    <div style="text-align: left; text-indent: 36pt; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">Ms. Brinda, age 58, has served as vice president and controller of the registrant since June 1, 2021.&#160; She has served in various accounting
      and financial positions (including officer positions) in various companies related to us and Contran since 1989.&#160; Immediately prior to June 1, 2021, Ms. Brinda served as vice president and controller of NL.</div>

    <div><br />
    </div>

    <div style="text-align: justify; text-indent: 36pt; font-family: 'Times New Roman', Times, serif; font-size: 10pt;">Ms. Samford and Ms. Brinda are employees of Contran and provide their services to the registrant under an intercorporate services
      agreement between the registrant and Contran.&#160; For a description of the intercorporate services agreement, see &#8220;Certain Relationships and Transactions&#8221; in the registrant&#8217;s 2021 proxy statement, which description is incorporated herein by reference.&#160;
      In addition, for a discussion of potential conflicts of interest of officers who serve more than one corporation, see &#8220;Certain Relationships and Transactions&#8221; in the 2021 proxy statement, which discussion is also incorporated herein by reference.</div>

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    <div style="text-align: center; font-family: 'Times New Roman', Times, serif; font-size: 12pt; font-weight: bold;">SIGNATURE</div>

    <div><br />
    </div>

    <div><br />
    </div>

    <div style="text-align: justify; text-indent: 36pt; font-family: 'Times New Roman', Times, serif; font-size: 12pt;">Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its
      behalf by the undersigned hereunto duly authorized.</div>

    <div><br />
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    <table cellspacing="0" cellpadding="0" id="z4df0f48972ea42cfba7ee9263632b022" style="font-family: 'Times New Roman', Times, serif; font-size: 10pt; width: 100%; text-align: left; color: #000000;">


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            <div style="text-align: justify; font-family: 'Times New Roman', Times, serif; font-size: 12pt; font-variant: small-caps; font-weight: bold;">Valhi, Inc.</div>
          </td>

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    <td style="width: 49.59%; vertical-align: top;">&#160;</td>

    <td style="width: 50.41%; vertical-align: top;">
            <div style="text-align: justify; font-family: 'Times New Roman', Times, serif; font-size: 12pt;">(Registrant)</div>
          </td>

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    <td style="width: 50.41%; vertical-align: top;">&#160;</td>

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    <td style="width: 50.41%; vertical-align: top;">&#160;</td>

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    <td style="width: 49.59%; vertical-align: top;">&#160;</td>

    <td style="width: 50.41%; vertical-align: top;">&#160;</td>

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    <td style="width: 49.59%; vertical-align: top;">&#160;</td>

    <td style="width: 50.41%; vertical-align: top;">&#160;</td>

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    <td style="width: 49.59%; vertical-align: top;">&#160;</td>

    <td style="width: 50.41%; vertical-align: top;">&#160;</td>

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    <td style="width: 50.41%; vertical-align: top; border-bottom: 2px solid black;">
            <div style="text-align: justify;"><span style="font-size: 12pt; font-family: 'Times New Roman', Times, serif;">By:</span><span style="display: inline-block; text-indent: 0px; font-size: 1px; width: 26.1pt">&#160;</span><span style="font-size: 12pt; font-family: 'Times New Roman', Times, serif;"><span style="font-size: 12pt; font-family: 'Times New Roman', Times, serif;">/s/ Jane Grimm</span><span style="display: inline-block; text-indent: 0px; font-size: 1px; width: 12pt">&#160;</span></span></div>
          </td>

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    <td style="width: 49.59%; vertical-align: top;">
            <div style="text-align: justify; font-family: 'Times New Roman', Times, serif; font-size: 12pt;">Date:&#160; June 2, 2021</div>
          </td>

    <td style="width: 50.41%; vertical-align: top;">
            <div style="text-align: justify; margin-left: 26.1pt; font-family: 'Times New Roman', Times, serif; font-size: 12pt; font-style: italic;">Jane Grimm, Vice President and Secretary</div>
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{"company-data": {"conformed-name": "VALHI INC /DE/", "cik": "0000059255", "assigned-sic": "2810", "irs-number": "870110150", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "8-K", "act": "34", "file-number": "001-05467", "film-number": "21989344"}, "business-address": {"street1": "5430 LBJ FRWY", "street2": "STE 1700", "city": "DALLAS", "state": "TX", "zip": "75240", "phone": "9722331700"}, "mail-address": {"street1": "THREE LINCOLN CENTER", "street2": "5430 LBJ FREEWAY SUITE 1700", "city": "DALLAS", "state": "TX", "zip": "75240-2620"}, "former-company": [{"former-conformed-name": "LLC CORP", "date-changed": "19870329"}, {"former-conformed-name": "LIBERTY LOAN CORP", "date-changed": "19800414"}]}
UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C.   20549
FORM
8-K
CURRENT REPORT
Pursuant to Section 13 or 15(d) of The Securities Exchange Act of 1934
Date of Report (Date of earliest event reported)
May 26, 2021
Valhi, Inc.
(Exact name of registrant as specified in its charter)
Delaware
1-5467
87-0110150
(State or other jurisdiction of incorporation)
(Commission
File Number)
(IRS Employer
Identification No.)
5430 LBJ Freeway
,
Suite 1700
,
Dallas
,
Texas
75240-2620
(Address of principal executive offices)
(Zip Code)
Registrant's telephone number, including area code
(
972
)
233-1700
(Former name or former address, if changed since last report.)
Check the appropriate box below if the Form 8-K filing is intended to simultaneously satisfy the filing obligation
      of the registrant under any of the following provisions (see General Instruction A.2):
☐
Written communications pursuant to Rule 425 under the Securities Act (17 CFR 230.425)
☐
Soliciting material pursuant to Rule 14a-12 under the Exchange Act (17 CFR 240.14a-12)
☐
Pre-commencement communications pursuant to Rule 14d-2(b) under the Exchange Act (17 CFR 240.14d-2(b))
☐
Pre-commencement communications pursuant to Rule 13e-4(c) under the Exchange Act (17 CFR 240.13e-4(c))
Securities registered pursuant to Section 12(b) of the Act:
Title of each class
Trading
Symbol(s)
Name of each exchange on which registered
Common stock
VHI
NYSE
Indicate by check mark whether the registrant is an emerging growth company as defined in Rule 405 of the Securities Act of 1933 (17 CFR §230.405) or Rule
        12b-2 of the Securities Exchange Act of 1934 (17 CFR §240.12b-2).
Emerging growth company
☐
If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for complying
        with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act.
☐
Item 5.02
Departure of Directors or Certain Officers; Election of Directors; Appointment of Certain Officers; Compensatory Arrangements of Certain Officers.
On May 26, 2021, James W. Brown, executive vice president and chief financial officer of the registrant, provided notice to the
      registrant of his retirement, effective as of June 1, 2021, as chief financial officer of the registrant.  In connection with his retirement as chief financial officer of the registrant, Mr. Brown also provided notice to Kronos Worldwide, Inc.
      ("Kronos Worldwide"), an affiliate of the registrant, of his retirement as chief financial officer of Kronos Worldwide as of June 1, 2021.  Following such retirements, Mr. Brown continues to be employed by Contran Corporation ("Contran"), the
      privately-held parent corporation of the registrant, and to serve as executive vice president of the registrant, Kronos Worldwide and Contran.
Following such retirement notice of Mr. Brown, the registrant's board of directors took action, also effective as of June 1, 2021, to:
•
elect Amy Allbach Samford as senior vice president and chief financial officer of the registrant; and
•
elect Patty S. Brinda as vice president and controller of the registrant.
Effective as of June 1, 2021, Michael S. Simmons, who formerly served as vice president and chief accounting officer of the registrant,
      became senior vice president, finance of the registrant, Kronos Worldwide and Contran and senior vice president and chief financial officer of CompX International Inc. ("CompX"), an affiliate of the registrant. Upon Ms. Brinda's election, Mr. Simmons
      ceased serving as the registrant's principal accounting officer.
Ms. Samford, age 47, has served as senior vice president and chief financial officer of the registrant since June 1, 2021.  She previously
      served as the registrant's vice president and controller from 2016 to June 2021.  She currently serves as senior vice president and chief financial officer of Contran and the registrant's affiliate NL Industries, Inc. ("NL").  Ms. Samford has served
      in various accounting and financial positions (including officer positions) in various companies related to us and Contran since 2006.  Immediately prior to June 1, 2021, Ms. Samford served as vice president and chief financial officer of each of NL
      and CompX.
Ms. Brinda, age 58, has served as vice president and controller of the registrant since June 1, 2021.  She has served in various accounting
      and financial positions (including officer positions) in various companies related to us and Contran since 1989.  Immediately prior to June 1, 2021, Ms. Brinda served as vice president and controller of NL.
Ms. Samford and Ms. Brinda are employees of Contran and provide their services to the registrant under an intercorporate services
      agreement between the registrant and Contran.  For a description of the intercorporate services agreement, see "Certain Relationships and Transactions" in the registrant's 2021 proxy statement, which description is incorporated herein by reference. 
      In addition, for a discussion of potential conflicts of interest of officers who serve more than one corporation, see "Certain Relationships and Transactions" in the 2021 proxy statement, which discussion is also incorporated herein by reference.
SIGNATURE
Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its
      behalf by the undersigned hereunto duly authorized.
Valhi, Inc.
(Registrant)
By:
/s/ Jane Grimm
Date:  June 2, 2021
Jane Grimm, Vice President and Secretary