We investigate the signals of a supersymmetric scenario where the lighter
tau-sneutrino is the lightest supersymmetric particle, while the lighter
stau-state is the next lightest. We confirm that such a scenario can be
motivated within the framework of minimal supergravity, with just the addition
of a right-chiral neutrino superfield. Such a spectrum leads to rather unusual
signals of supersymmetry, showing stable tracks of the stau in the muon
chambers. We have studied two types of signals, namely, (a) two or more hard
jets and two stau tracks, and (b) hard jets with two muons and two stau tracks.
We demonstrate that the stau tracks can be distinguished from the muonic ones
through proper kinematic cuts which also enable one to remove all standard
model backgrounds.Comment: Latex2E, 18 pages, 8 eps figures included (To appear in Phys.Rev. D