  We study neutrino masses in the framework of the supersymmetric inverse
seesaw model. Different from the non-supersymmetric version a minimal
realization with just one pair of singlets is sufficient to explain all
neutrino data. We compute the neutrino mass matrix up to 1-loop order and show
how neutrino data can be described in terms of the model parameters. We then
calculate rates for lepton flavour violating (LFV) processes, such as $\mu \to
e \gamma$, and chargino decays to singlet scalar neutrinos. The latter decays
are potentially observable at the LHC and show a characteristic decay pattern
dictated by the same parameters which generate the observed large neutrino
angles.
