  Supersymmetric scenarios with a very weakly interacting lightest
superparticle (LSP) - like the gravitino or axino - naturally give rise to a
long-lived next-to-LSP (NLSP). In the case of a stau NLSP, the scenario shows
up in a very prominent way at colliders. We present the LHC sensitivity for
these classes of scenarios in the framework of simplified models. This allows
for deriving robust limits on the masses of the lightest stau, the gluino and
squarks.
