  The electric dipole moment of the muon (d_mu) is evaluated in supersymmetric
models with nonzero neutrino masses and large neutrino mixing arising from the
seesaw mechanism. It is found that if the seesaw mechanism is embedded in the
framework of a left-right symmetric gauge structure, the interactions
responsible for the right-handed neutrino Majorana masses lead to an
enhancement in d_mu. We find d_mu as large as 5. 10^{-23} ecm with a correlated
value of (g-2) = 13. 10^{-10}, even for low values of tan beta. This should
provide a strong motivation for improving the edm of the muon to the level of
10^{-24} ecm as has recently been proposed.
