We compute the scattering rates for the lightest neutralino χ 0 1 in the forthcoming germanium ( 73 Ge+ 76 Ge) detector and a proposed lead detector ( 207 Pb), within the framework of SU (5) × U (1) supergravity. We find that in only a small portion ( < ∼ 10%) of the parameter spaces of this class of models, are the rates in the germanium detector above the expected initial experimental sensitivity of 0.1 events/kg/day. However, a much larger portion ( < ∼ 40%) of the parameter spaces could be probed with an improved background rejection capability (0.01 events/kg/day) and/or a more sensitive detector ( 207 Pb).