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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 stabilising 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.
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