  We investigate the possibility of large CP- violating phases in the soft
breaking terms derived in superstring models. The bounds on the electric dipole
moments (EDM's) of the electron and neutron are satisfied through cancellations
occuring because of the structure of the string models. Three general classes
of four-dimensional string models are considered: (i) orbifold
compactifications of perturbative heterotic string theory, (ii) scenarios based
on Ho\v{r}ava-Witten theory, and (iii) Type I string models (Type IIB
orientifolds). Nonuniversal phases of the gaugino mass parameters greatly
facilitate the necessary cancellations among the various contributions to the
EDM's; in the overall modulus limit, the gaugino masses are universal at tree
level in both the perturbative heterotic models and the Ho\v{r}ava-Witten
scenarios, which severely restricts the allowed regions of parameter space.
Nonuniversal gaugino masses do arise at one-loop in the heterotic orbifold
models, providing for corners of parameter space with ${\cal O}(1)$ phases
consistent with the phenomenological bounds. However, there is a possibility of
nonuniversal gaugino masses at tree level in the Type I models, depending on
the details of the embedding of the SM into the D- brane sectors. We find that
in a minimal model with a particular embedding of the Standard Model gauge
group into two D- brane sectors, viable large phase solutions can be obtained
over a wide range of parameter space.
