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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.

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