Abstract: 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 μ-> 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.