Co-Monolayers, prepared by MBE on Cu (111) -surfaces at room temperature and covered by Cu, are ferromagnetic with a Curie-temperature of about 430 K. They are magnetized perpendicularly because of a strong perpendicular magnetic surface anisotropy of the Cu/Co (111) -interface. They provide a remarkably good representation of the 2-dimensional Ising Model. The indirect coupling between these perpendicularly magnetized ferromagnetic monolayers was investigated using samples of type Cu (111) /lCo/DçuCu/lCo/Cu, containing Co/Cu/Co-trilayers composed of Co-Monolayers and a spacer consisting of DCu atomic layers of Cu (111). Torsion oscillation magnetometry of these samples showed clearly a coupling between the monolayers with an oscillatory dependence on DCu. The amplitude of the oscillation is strongly reduced if the coupled Co-films consist of 5 ML instead of 1 M.L. The present controversy on the presence or absence of antiferromagnetic and oscillatory indirect coupling in the Co/Cu (111) -system is discussed in the light of these experiments. The discussion shows that the oscillatory coupling is an intrinsic property of ideal (111)-structures, and can be understood by the RKKY-type theory of indirect coupling between ferromagnetic Monolayers. The usual application of this theory to the coupling between thicker films is justified. However, in the fcc (111) -system there is apparently a specific barrier against complete coalescence, resulting in a tendency to retain holes and channels in the Cu-spacer. This tendency is stronger in flat single-crystal samples than in sputtered films with high densities of atomic steps. Apparently, this results in competing ferromagnetic hole coupling which may more or less completely obscure the intrinsic oscillatory coupling, preferentially in samples grown on extremely flat single crystal surfaces.