  The many-body Green's function theory developed in our previous work for
treating the reorientation of the magnetization of thin ferromagnetic films is
extended to include the exchange anisotropy. This leads to additional momentum
dependencies which require some non-trivial changes in the formalism. The
theory is developed for arbitrary spin values S and for multilayers. The
effects of the exchange anisotropy and the single-ion anisotropy, which was
treated in our earlier work, on the magnetic properties of thin ferromagnetic
films are compared.
