Resonant-mass detectors of gravitational radiation have been developed that are reliably operating at liquid helium temperature (4.2K) with sensitivities h ~ 6x10-19, where h is the dimensionless strain amplitude of the waves. At this sensitivity level we do not expect to detect gravitational wave signals from anything but the rarest astrophysical events. For the past several years the Stanford group has been designing and constructing an ultralow temperature (50mK) detector. It is expected to have an initial sensitivity of at least h=10-19 and eventually less than 10-20, sufficient to detect gravitational radiation from plausible but rare astrophysical events that could occur in our galaxy or its immediate vicinity. Success in this endeavour could bring direct confirmation of an important prediction of Einstein's General Theory of Relativity and also open an entirely new window on our universe that will yield information not available from optical, radio, infrared, x-ray, or gamma-ray astronomy. The key elements of the research program during the next three years are reliable operation of the ultralow temperature (50mk) detector now nearing completion, operation of this detector in coincidence with other gravitational wave detectors and correlate the output with other electromagnetic (e.g., gamma-ray burst) and neutrino burst detectors, continuing research to advance the state-of-the-art in superconductive modulated-inductance transducers and SQUIDs.