**EXHIBIT      31.2**

| 1. | I                have reviewed this annual report on Form 10-K of PaineWebber R&D                Partners III, L.P. (the“Partnership”); |
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| 2. | Based                on my knowledge, this annual 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                annual report; |
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| 3. | Based                on my knowledge, the financial statements, and other financial information                included in this annual report, fairly present in all material respects                the financial condition, results of operations and cash flows of                the                Partnership as of, and for, the periods presented in this annual                report; |
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| 4. | The                Partnership’s other certifying officers and I are responsible for                establishing and maintaining disclosure controls and procedures (as                defined in Exchange Act Rules 13(a)-15(e) and 15(d)-15(e) for the                Partnership and we have: |
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|  | (a) | designed                    such disclosure controls and procedures to ensure that material                    information relating to the Partnership is made known to us by                    others                    within the Partnership, particularly during the period in which                    this                    annual report is being                    prepared; |
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|  | (b) | evaluated                      the effectiveness of the Partnership’s disclosure controls and procedures                      as of a date within 90 days prior to the filing date of this                      annual report                      (the “Evaluation Date”); and |
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|  | (c) | disclosed                        in the annual report any change in the Partnership’s internal control over                        financial reporting (as defined in Exchange Act Rules 13(a)-15(f)                        and                        15(d)-15(f)) that occurred during the Partnership’s fourth fiscal quarter                        that has materially affected, or is reasonably likely to                        materially affect                        the Partnership’s internal control over financial                        reporting; |
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| 5. | The                Partnership’s other certifying officers and I have disclosed, based on our                most recent evaluation, to the Partnership’s auditors and the audit                committee of the board of directors of the Partnership’s general partner                (or persons performing the equivalent                function): |
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|  | (a) | all                    significant deficiencies in the design or operation of internal                    controls                    which could adversely affect the Partnership’s ability to record, process,                    summarize and report financial data and have identified for the                    Partnership’s auditors any material weaknesses in internal controls;                    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 Partnership’s internal                    controls. |
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|   |                                                                                                                                                                                                                                                 | /s/ Rosemarie              Albergo   |
|   | Name:                Rosemarie AlbergoTitle:                Assistant Treasurer (Principal Financial and Accounting Officer)                of                PaineWebber Development Corporation, General                Partner of the Partnership |

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