  $\mu^{+} \to e^{+} \gamma$ and $\mu^{+} \to e^{+}e^{+}e^{-}$ processes are
analyzed in detail with polarized muons in supersymmetric grand unified
theories. We first present Dalitz plot distribution for $\mu^{+} \to
e^{+}e^{+}e^{-}$ decay based on effective Lagrangian with general
lepton-flavor-violating couplings and define various P- and T-odd asymmetries.
We calculate branching ratios and asymmetries in supersymmetric SU(5) and
SO(10) models taking into account complex soft supersymmetry breaking terms.
Imposing constraints from experimental bounds on the electron, neutron and
atomic electric dipole moments, we find that the T-odd asymmetry for $\mu^{+}
\to e^{+}e^{+}e^{-}$ can be 15% in the SU(5) case. P-odd asymmetry with respect
to muon polarization for $\mu^{+} \to e^{+} \gamma$ varies from -20% to -100%
for the SO(10) model while it is $+100%$ in the SU(5) case. We also show that
the P-odd asymmetries in $\mu^{+} \to e^{+}e^{+}e^{-}$ and the ratio of
$\mu^{+} \to e^{+}e^{+}e^{-}$ and $\mu^{+} \to e^{+} \gamma$ branching
fractions are useful to distinguish different models.
