Since its discovery more than 20 years ago1,2, variability of extragalactic radio sources on timescales of weeks to years has been the subject of many investigations. Little is known, however, about radio variability of extragalactic sources on timescales of less than a few days. Variations on timescales of hours—mostly at millimetre wavelengths—have been reported for several sources3–6. Heeschen et al.7 have found variability with amplitudes of up to 12% in less than 1 day at 11-cm wavelength in a sample of northern (δ≥60°) compact sources. We have continued these observations at wavelengths of 6 and llcm using the 100-m telescope of the Max-Planck-Institut fur Radioastronomie and report here the results for two sources. The quasar QSO0917 + 62 showed variations with amplitudes of up to 23% in ∼24 hours, which were correlated at the two wavelengths; in the BL Lac object 0716 + 71 we found variations with amplitudes of 7–11%. We discuss intrinsic effects, gravitational lensing and scattering in the interstellar medium as possible explanations for rapid radio variability.