  In supersymmetric models, there are new CP violating phases which, if
unsuppressed, would give a too large neutron electric dipole moment. We examine
the possibility of small SUSY phases in string-inspired supergravity models in
which supersymmetry is broken by the auxiliary components of the dilaton and
moduli superfields. It is found that the SUSY phases can be suppressed by a
small factor governing the breakdown of the approximate Peccei Quinn symmetries
nonlinearly realized for the moduli superfields that participate in
supersymmetry breaking. In many cases, the symmetry breaking factors are
exponentially small for moderately large values of the moduli, leading to small
phase values in a natural way.
