|   | Exhibit      31.1 |
|--------|-------------------|

| 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; |
|----|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

| 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 Valhi, Inc.      as of, and for, the periods presented in this  report; |
|----|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

| 4) | Valhi,      Inc.’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      Valhi, Inc. and we have: |
|----|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

| 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 Valhi, Inc., 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; |
|----|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

| 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; |
|----|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

| c) | Evaluated      the effectiveness of Valhi, Inc.'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 |
|----|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

| d) | Disclosed      in this report any change in Valhi, Inc.’s internal control over financial      reporting that occurred during the registrant’s most recent fiscal quarter      (Valhi, Inc.’s fourth fiscal quarter in the case of an Annual Report) that      has materially affected, or is reasonably likely to materially affect,      Valhi, Inc.’s internal control over financial reporting;    and |
|----|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

| 5) | Valhi,      Inc.'s other certifying officer and I have disclosed, based on our most      recent evaluation of internal control over financial reporting, to the      Valhi, Inc.'s auditors and the audit committee of Valhi, Inc.'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 Valhi, Inc.'s ability to record,      process, summarize and report financial information;  and |
|----|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

| b) | Any      fraud, whether or not material, that involves management or other      employees who have a significant role in Valhi, Inc.'s internal control      over financial reporting. |
|----|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|