  Supersymmetry with bilinear R-parity violation provides a predictive
framework for neutrino masses and mixings in agreement with current neutrino
oscillation data. The model leads to striking signals at future colliders
through the R-parity violating decays of the lightest supersymmetric particle.
Here we study charged scalar lepton decays and demonstrate that if the scalar
tau is the LSP (i) it will decay within the detector, despite the smallness of
the neutrino masses, (ii) the relative ratio of branching ratios Br({tilde
tau}_1 --> e sum nu_i)/ Br({tilde tau}_1 --> mu sum nu_i) is predicted from the
measured solar neutrino angle, and (iii) scalar muon and scalar electron decays
will allow to test the consistency of the model. Thus, bilinear R-parity
breaking SUSY will be testable at future colliders also in the case where the
LSP is not the neutralino.
