  The constraints of electric dipole moments (EDMs) of electron and neutron on
the parameter space in supergravity (SUGRA) models with nonuniversal gaugino
masses are analyzed. It is shown that with a light sparticle spectrum, the
sufficient cancellations in the calculation of EDMs can happen for all phases
being order of one in the small tan$\beta$ case and all phases but $\phi_{\mu}$
($|\phi_{\mu}| <\sim \pi/6$) order of one in the large tan$\beta$ case. This is
in contrast to the case of mSUGRA in which in the parameter space where
cancellations among various SUSY contributions to EDMs happen $|\phi_{\mu}|$
must be less than $\pi/10$ for small $tan\beta$ and ${\cal{O}}(10^{-2})$ for
large $tan\beta$. Direct CP asymmetries and the T-odd polarization of lepton in
$B\to X_s l^+l^-$ are investigated in the models. In the large tan$\beta$ case,
$A_{CP}^2$ and $P_N$ for l=$\mu$ ($\tau$) can be enhanced by about a factor of
ten (ten) and ten (three) respectively compared to those of mSUGRA.
