  We show that, in perturbative string models where the source of CP violation
is a complex vacuum expectation value (v.e.v.) for one or more compactification
moduli, CP is conserved if a CP transformation acting on the modulus values is
an element of a target-space (self-)duality group. Where the duality group is
SL(2,Z) the result confirms a conjecture of Bailin et al. that CP is conserved
for v.e.v.'s of the T modulus on the boundary of the fundamental domain, and
generalises Giedt's result on the removability of complex Yukawa couplings in
such models. Our result applies to any model of spontaneous CP violation where
the CP-odd scalar transforms under a symmetry that is not explicitly broken. We
consider whether similar results could be obtained in ``brane worlds''.
