The itinerant electron subsystem of the superlattice of nonmagnetic mediators and magnetic slabs is considered. It is argued that the electrons are confined (in the transverse to the interface direction) in a set of quantum wells. These sets are different for the ferro- and antiferromagnetic ordering of the slabs. As a result, the difference of the energies (per unit volume) for these two types of orderings, which depend on the mediator thickness, change sign regularly. Such behaviour reproduces the oscillations of the antiferromagnetic exchange coupling strength. A qualitative description of the giant magnetoresistance is presented. The results of preliminary calculations are in reasonable correspondence with the experimental data. © 1994.