  In the light of the recent muon (g_mu-2) result by the E821 experiment at the
Brookhaven National Laboratory, we study the event rates of the charged
lepton-flavour-violating (LFV) processes in the supersymmetric standard model
(SUSY SM) with the heavy right-handed neutrinos (SUSY see-saw model). Since the
left-handed sleptons get the LFV masses via the neutrino Yukawa interaction in
this model, the event rate of mu->e gamma and the SUSY-SM correction to
(g_mu-2)/2 (\delta a_mu^{SUSY}) are strongly correlated. When the left-handed
sleptons have a LFV mass between the first and second generations
((m^2_L)_{12}) in the mass matrix, it should be suppressed by \sim 10^{-3}
({10^-9}/\delta a_mu^{SUSY}) compared with the diagonal components
(m_{SUSY}^2), from the current experimental bound on mu-> e gamma. The recent
(g_mu-2) result indicates {\delta a_mu^{SUSY}}\sim 10^{-9}. The future charged
LFV experiments could cover (m^2_L)_{12}/m_{SUSY}^2\gsim 10^{-(5-6)}. These
experiments will give a significant impact on the flavour models and the
SUSY-breaking models. In the SUSY see-saw model (m^2_L)_{12} is proportional to
square of the tau-neutrino Yukawa-coupling constant. In the typical models
where the neutrino-oscillation results are explained and the top-quark and
tau-neutrino Yukawa couplings are unified at the GUT scale, a large LFV mass of
(m^2_L)_{12}/m_{SUSY}^2\gsim 10^{-4} is generated, and the large LFV event
rates are predicted. We impose a so-called no-scale condition for the
SUSY-breaking parameters at the GUT scale, which suppresses the FCNC processes,
and derive the conservative lower bound on mu-> egamma. The predicted Br(mu-> e
gamma) could be covered at the future LFV experiments.
