  The expected event rates for ${\tilde Z_{1}}$ dark matter for a variety of
dark matter detectors are studied over the full parameter space with tan
$\beta\leq$ 20 for supergravity grand unified models. Radiative breaking
constraints are implemented and effects of the heavy netural Higgs included as
well as loop corrections to the neutral Higgs sector. The parameter space is
restricted so that the ${\tilde Z_{1}}$ relic density obeys 0.10
$\leq\Omega_{\tilde Z_{1}}h^2\leq 0.35$, consistent with the COBE data and
astronomical determinations of the Hubble constant. It is found that the best
detectors sensitive to coherrent ${\tilde Z_{1}}$ scattering (e.g. Pb) is about
5-10 more sensitive than those based on incoherrent spin dependent scattering
(e.g. CaF). In general, the dark matter detectors are most sensistive to the
large tan $\beta$ and small $m_o$ and $m_{\tilde g}$ sector of the parameter
space.
