  We perform an exhaustive study of the role neutrino telescopes could play in
the discovery and exploration of supersymmetric extensions of the Standard
Model with a long-lived stau next-to-lightest superparticle. These staus are
produced in pairs by cosmic neutrino interactions in the Earth matter. We show
that the background of stau events to the standard muon signal is negligible
and plays no role in the determination of the cosmic neutrino flux. On the
other hand, one can expect up to 50 pair events per year in a cubic kilometer
detector such as IceCube, if the superpartner mass spectrum and the high-energy
cosmic neutrino flux are close to experimental bounds.
