  We establish both a local and a global well-posedness theories for the
nonlinear Hartree-Fock equations and its reduced analog in the setting of the
modulation spaces on $\mathbb R^d$. In addition, we prove similar results when
a harmonic potential is added to the equations. In the process, we prove the
boundedeness of certain multilinear operators on products of the modulation
spaces which may be of independent interest.
