  The cosmological relic density of the lightest supersymmetric particle (LSP)
of type I string derived model is calculated. This model can accommodate large
values of CP violating phases, and the electron and neutron electric dipole
moments satisfy the experimental constraint. We show that the constraint from
the electric dipole moment on the ratio between the gaugino masses implies that
the mass of the LSP, which is bino like, is close to the lightest chargino. The
co-annihilation between them is very important to reduce the LSP relic density
to an interesting region. We show that the SUSY phases, although they are
large, have no significant effect on the relic density and on the the upper
bound imposed on the LSP mass. However, they are very significant for the
detection rates. We emphasize that the phase of the trilinear coupling increase
the direct and indirect detection rates.
