  We derive the duality symmetries relevant to moduli dependent gauge coupling
constant threshold corrections, in Coxeter $ {\bf Z_N} $ orbifolds. We consider
those orbifolds for which the point group leaves fixed a 2-dimensional
sublattice $\Lambda_2$, of the six dimensional torus lattice $\Lambda_6$, where
$\Lambda_6 $ cannot be decomposed as $\Lambda_2 \bigoplus{\Lambda_4}.$
