Target space symmetries are studied for orbifold compactified string t
heories containing Wilson line background fields. The symmetries deter
mined are for those moduli which contribute to the string loop thresho
ld corrections of the gauge coupling constants. The groups found are s
ubgroups of the modular group PSL(2, Z) and depend on the choice of di
screte Wilson lines and the shape of the underlying six-dimensional la
ttice.