  Accumulation and annihilation of weakly interacting massive particles (WIMPs)
in the earth and the sun may be observed by the resulting neutrino signal. We
demonstrate that, for certain parts of the SUSY parameter space, present and
future neutrino telescopes can expect a higher rate of events due to
tau-neutrinos than of events due to muon-neutrinos. We show how
$\nu_{\tau}\leftrightarrow\nu_{\mu}$ oscillations, and in the case of the sun
also scattering, absorption and regeneration, modify the signal expectation. We
find that most currently proposed neutralino models predict equal or increased
muon fluxes if $\nu_{\tau}\leftrightarrow\nu_{\mu}$ oscillations are included.
