  We analyze the electric dipole moment of the electron ($d_e$), of the neutron
($d_n$) and of the muon ($d_{\mu}$) using the cancellation mechanism in the
presence of nonuniversalities of the soft breaking parameters. It is shown that
the nonuniversalities in the slepton sector produce a strong violation of the
scaling relation $d_{\mu}/d_e\simeq m_{\mu}/m_e$ in the cancellation region. An
analysis of $d_e, d_n$ and $d_{\mu}$ under the constraints of the current
experimental limits on $d_e$ and $d_n$ and under the constraints of the recent
Brookhaven result on $g_{\mu}-2$ shows that in the non-scaling region $d_{\mu}$
can be as large as ($10^{-24}-10^{-23}$)ecm and thus within reach of the
recently proposed Brookhaven experiment for a sensitive search for $d_{\mu}$ at
the level of $10^{-24}$ ecm.
