  The supersymmetric CP problem is studied within superstring-motivated
extensions of the MSSM with an additional U(1)' gauge symmetry broken at the
TeV scale. This class of models offers an attractive solution to the mu problem
of the MSSM, in which U(1)' gauge invariance forbids the bare mu term, but an
effective mu parameter is generated by the vacuum expectation value of a
Standard Model singlet S which has superpotential coupling of the form SH_uH_d
to the electroweak Higgs doublets. The effective mu parameter is thus
dynamically determined as a function of the soft supersymmetry breaking
parameters, and can be complex if the soft parameters have nontrivial
CP-violating phases. We examine the phenomenological constraints on the
reparameterization invariant phase combinations within this framework, and find
that the supersymmetric CP problem can be greatly alleviated in models in which
the phase of the SU(2) gaugino mass parameter is aligned with the soft
trilinear scalar mass parameter associated with the SH_uH_d coupling. We also
study how the phases filter into the Higgs sector, and find that while the
Higgs sector conserves CP at the renormalizable level to all orders of
perturbation theory, CP violation can enter at the nonrenormalizable level at
one-loop order. In the majority of the parameter space, the lightest Higgs
boson remains essentially CP even but the heavier Higgs bosons can exhibit
large CP-violating mixings, similar to the CP-violating MSSM with large mu
parameter.
