  We study the minimal version of the supersymmetric standard model with
spontaneous CP breaking. In this model, the KM matrix is real and contributions
to $\varepsilon$ arise from box diagrams involving squarks. We analyze the
region of the parameter space which corresponds to values for $\varepsilon$,
$\varepsilon^\prime/\varepsilon$ and the neutron electric dipole moment (NEDM)
in agreement with the experimental data. We show that the CP violating phases
must be of $\calo (10^{-2})$ and the NEDM lies near its present experimental
limit.
