We study the CP phases of the soft supersymmetry breaking terms in string-i
nspired models with nonuniversal trilinear couplings. We show that such non
universality plays an important role on all CP violating processes. In part
icular these new supersymmetric sources of CP violation may significantly c
ontribute to the observed CP phenomena in kaon physics while respecting the
severe bound on the electric dipole moment of the neutron. [S0556-2821(99)
03217-8].