  We consider SUSY extensions of the standard model where the gravitino is the
dark-matter particle and the stau is long lived. If there is a significant mass
gap with squarks and gluinos, the staus produced at hadron colliders tend to be
fast (beta>0.8), and the searches based on their delay in the time of flight or
their anomalous ionization become less effective. Such staus would be
identified as regular muons with the same linear momentum and a slightly
reduced energy. Compared to the usual SUSY models where a neutralino is the
LSP, this scenario implies (i) more leptons (the two staus at the end of the
decay chains), (ii) a strong e-mu asymmetry, and (iii) less missing E_T (just
from neutrinos, as the lightest neutralino decays into stau). We study the
bounds on this SUSY from current LHC analyses (same-sign dileptons and
multilepton events) and discuss the best strategy for its observation.
