  The possibility of spontaneous breaking of CP symmetry by the expectation
values of orbifold moduli is investigated with particular reference to $CP$
violating phases in soft supersymmetry breaking terms. The effect of different
mechanisms for stabilizing the dilaton and the form of the non-perturbative
superpotential on the existence and size of these phases is studied. Models
with modular symmetries which are subgroups of $PSL(2,Z)$, as well as the
single overall modulus $T$ case with the full $PSL(2,Z)$ modular symmetry, are
discussed. Non-perturbative superpotentials involving the absolute modular
invariant $j(T)$, such as may arise from F-theory compactifications, are
considered.
