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The temporal stability of trapped transport current in annular thin film Tl/sub 2/Ba/sub 2/CaCu/sub 2/O/sub 8/ (TBCCO) and YBa/sub 2/Cu/sub 3/O/sub 7/ (YBCO) wafers has been accurately measured and has been found to be of suitable quality for the stringent requirements of nuclear magnetic resonance (NMR) magnets. No detectable decay, to the limit of the experimental apparatus (2*10/sup -14/ /spl Omega/), was detected in those wafers with transport current at or below the critical current density J/sub c/. The critical current density, as previously determined from 12 /spl mu/m meander lines, was confirmed in a wafer with a width of 1.9 cm. The profile of trapped magnetic field resulting from induced current was modeled in order to assess its effect on the uniformity of an NMR magnet.