  We evaluate the fluxes of up--going muons detectable in a neutrino telescope
and due to the annihilation of relic neutralinos in the Earth and in the Sun,
taking realistically into account the fact that neutralinos might provide only
a fraction of the local (solar neighbourhood) dark matter (DM). We determine
the relation between the exposure $A t$ of the neutrino telescope ($A$ being
the telescope area, $t$ the live time) and the explorable range of the
neutralino mass and composition, when the signal--to--background ratio is
optimized by an appropriate angular selection.
