Exhibit
31.1

CERTIFICATION OF PRINCIPAL EXECUTIVE
OFFICER



I, Hollis M. Greenlaw, certify that:



| | 1. | I have reviewed this quarterly report on Form 10-Q of United Development Funding III, L.P.;
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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 our 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 functions):
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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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|Dated this 14th day of August, 2012. |                                                                                                                                                                                                                     
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|                                     | /s/ Hollis M. Greenlaw                                                                                                                                                                                              
|                                     | Hollis M. Greenlaw                                                                                                                                                                                                  
|                                     | Chief Executive Officer of UMTH Land Development, L.P., sole general partner of the Registrant, and President and Chief Executive Officer of UMT Services, Inc., sole general partner of UMTH Land Development, L.P.