EXHIBIT 31.1
                                                                    ------------



CERTIFICATIONS

I, Stephen R. Dyer, certify that:

1.       I have reviewed this annual report on Form 10-K of PaineWebber R&D
         Partners III, L.P. (the "Partnership");

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;

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;

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:

         (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;

         (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

         (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;

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):

         (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

         (b)      any fraud, whether or not material, that involves
                  management or other employees who have a significant role in
                  the Partnership's internal controls.


Date:  March 30, 2004
                                         /s/ Stephen R. Dyer
                                         ---------------------------------------
                                         Name:  Stephen R. Dyer
                                         Title: President of PaineWebber
                                                Development Corp., General
                                                Partner of the Partnership