There has for some time been evidence of variability in radiochemical solar neutrino measurements, but this evidence has seemed suspect since the cerenkov experiments have not shown similar evidence of variability. The present re-analysis of Super-Kamiokande data shows strong evidence of r-mode oscillations. The frequencies of these oscillations correspond to a region with a sidereal rotation rate of 13.97 year-1, not far from the value 13.88 year-1 found some time ago in Homestake data, or 13.87 year-1 found recently in GALLEX data. These estimates are incompatible with the rotation rate in the convection zone, but fully compatible with current estimates of the rotation rate in the radiative zone, including the solar core. These results are suggestive of variability originating in the core from fluctuating and asymmetric nuclear burning.