  CP-violating phases which contribute to the electric dipole moment(EDM) of
the neutron are considered in the context of orbifold compactificationof the
heterotic string. In particular, we study the situation where CP is
spontaneously broken by moduli fields acquiring, in general, complex
expectation values at the minimum of duality invariant low energy effective
potentials. We show, by explicit minimization of such a potential in the case
of the ${\bf Z}_{6}-{\rm IIb}$ orbifold, that it is the presence of so called
Green-Schwarz anomaly coefficients $\delta_{\rm GS}^{i} $, that leads to
significant CP violating expectation values of the moduli. By evaluating the
soft supersymmetry breaking moduli dependent $A$ and $B$ terms in this model,
we find that the experimental bounds $\Phi (A) $, $ \Phi (B) $ $\leq 5 \times
10^{-3} $ are exceeded for a particular range of values of the auxiliary field
of the $S$ modulus.
