| Exhibit      31.2 |
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| 1) | I      have reviewed this Annual Report on Form 10-K of Valhi,    Inc.; |
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| 2) | Based      on my knowledge, this report does not contain any untrue statement of a      material fact or omit to state a material fact necessary to make the      statements made, in light of the circumstances under which such statements      were made, not misleading with respect to the period covered by this      report; |
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| 3) | Based      on my knowledge, the financial statements, and other financial information      included in this report, fairly present in all material respects the      financial condition, results of operations and cash flows of the      registrant as of, and for, the periods presented in this      report; |
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| 4)  | The      registrant’s other certifying officer and I are responsible for      establishing and maintaining disclosure controls and procedures (as      defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal      control over financial reporting (as defined in Exchange Act Rules      13a-15(f) and 15d-15(f)) for the registrant and have: |
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|   | a) | Designed      such disclosure controls and procedures, or caused such disclosure      controls and procedures to be designed under our supervision, to ensure      that material information relating to the registrant, including its      consolidated subsidiaries, is made known to us by others within those      entities, particularly during the period in which this report is being      prepared; |
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|   | b) | Designed      such internal control over financial reporting, or caused such internal      control over financial reporting to be designed under our supervision, to      provide reasonable assurance regarding the reliability of financial      reporting and the preparation of financial statements for external      purposes in accordance with generally accepted accounting      principles; |
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|   | c) | Evaluated      the effectiveness of the registrant’s disclosure controls and procedures      and presented in this report our conclusions about the effectiveness of      the disclosure controls and procedures, as of the end of the period      covered by this report based on such evaluation;  and |
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|   | d) | Disclosed      in this report any change in the registrant’s internal control over      financial reporting that occurred during the registrant’s most recent      fiscal quarter (the registrant’s fourth fiscal quarter in the case of an      annual report) that has materially affected, or is reasonably likely to      materially affect, the registrant’s internal control over financial      reporting; and |
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| 5)  | The      registrant’s other certifying officer and I have disclosed, based on our      most recent evaluation of internal control over financial reporting, to      the registrant’s auditors and the audit committee of the registrant’s      board of directors (or persons performing the equivalent      function): |
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|   | a) | All      significant deficiencies and material weaknesses in the design or      operation of internal control over financial reporting which are      reasonably likely to adversely affect the registrant’s ability to record,      process, summarize and report financial information;  and |
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|   | b) | Any      fraud, whether or not material, that involves management or other      employees who have a significant role in the registrant’s internal control      over financial reporting. |
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