The radio and optical positions of the stars HR 1099 and UX Ari have been measured at nearby epochs. The radio positions are referred to background quasars, and the optical positions are on the FK4 system. The radio and optical coordinates agree within the 0arcsec.05 accuracy of the optical measurements, except for a discrepancy of 0arcsec.27±0arcsec.06 in the right ascension of HR 1099. The latter may result from the combined effects of local deviations in the two reference frames, atmospheric effects, or differences in source structure at radio and optical wavelengths. The radio and optical measurements of the proper motions agree well.