  We study a supersymmetric scenario where the lighter tau-sneutrino is the
lightest supersymmetric particle, while the lighter stau-state is the next
lightest. 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 study the event
characteristics of the long-lived staus at the LHC and 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.
