  In this work the following lepton flavor violating $\tau$ and $\mu$ decays
are studied: $\tau^- \to \mu^- \mu^- \mu^+$, $\tau^- \to e^- e^- e^+$, $\mu^-
\to e^- e^- e^+$, $\tau^- \to \mu^- \gamma$, $\tau^- \to e^- \gamma$ and $\mu^-
\to e^- \gamma$. We work in a constrained supersymmetric scenario with
universal soft breaking terms and where the MSSM particle content is extended
by the addition of three heavy right handed Majorana neutrinos and their
supersymmetric partners. The generation of neutrino masses is done via the
seesaw mechanism. We analize all these lepton flavor violating decays in terms
of the relevant input parameters, which are the usual mSUGRA parameters and the
seesaw parameters. In the numerical analysis compatibility with the most recent
experimental upper bounds on all these $\tau$ and $\mu$ decays, with the
neutrino data, and with the present lower bounds on the supersymmetric particle
masses are required. Two typical scenarios with degenerate and hierarchical
heavy neutrinos are considered. We will show here that the minimal supergravity
and seesaw parameters do get important restrictions from these $\tau$ and $\mu$
decays in the hierarchical neutrino case.
