  We study unconventional decays of the top-quark in the framework of SUSY
models with spontaneously broken R-parity. In particular we discuss an
effective theory which consists of the MSSM plus bilinearly broken R-parity. We
demonstrate that the decay modes t -> stau + b and t -> tau + sbottom can have
large branching ratios even in scenarios where the tau-neutrino mass is very
small. We show that existing Tevatron data already probe the theoretical
parameters, with promising prospects for further improvement at the Run 2 of
the Tevatron.
