  We show that an intermediate gauge symmetry breaking scale can be a
significant source of electric dipole moments for the electron and neutron in
supersymmetric grand unified theories. New phases, similar to that of the CKM
matrix, appear which do not arise from the supersymmetry (SUSY) breaking
operators. To illustrate, we choose some grand unified SUSY models having an
intermediate gauge symmetry breaking scale with some attractive features. We
also show how well the $b-\tau$ unification hypothesis works in this class of
models.
