  We derive the moduli dependent threshold corrections to gauge couplings in
toroidal orbifold compactifications. The underlying six dimensional torus
lattice of the heterotic string theory is not assumed ---as in previous
calculations--- to decompose into a direct sum of a four--dimensional and a
two--dimensional sublattice, with the latter lying in a plane left fixed by a
set of orbifold twists. In this more general case the threshold corrections are
no longer automorphic functions of the modular group, but of certain congruence
subgroups of the modular group. These groups can also be obtained by studying
the massless spectrum; moreover they have larger classes of automorphic
functions. As a consequence the threshold corrections cannot be uniquely
determined by symmetry considerations and certain boundary conditions at
special points in the moduli space, as was claimed in previous publications.
