The constraints of electric dipole moments (EDMs) of the electron and neutron on parameter space in supergravity (SUGRA) models with nonuniversal gaugino masses are analyzed. It is shown that, with a light sparticle spectrum, a sufficient cancellation in the calculation of EDMs can happen for all phases of order I in the small tan beta case and all phases but phi mu (\phi mu\less than or similar to pi/6) of order 1 in the large tan beta case. This is in contrast with 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 O(10(-2)) for large tan beta. Direct CP asymmetries and the T-odd normal polarization of the lepton in B-->X(s)l(+) l(-) are investigated in these 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 10 (10) and 10 (3), respectively, compared to those of MSUGRA.
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