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