The energy-level structure of superlattices in a magnetic field parallel and perpendicular to the layers, when the periodicities are comparable to the cyclotron orbit radius, is studied; experimentally with interband excitation spectroscopy and theoretically with the quasi-classical quantization of the ' superlattice bandstructure in a magnetic field as well as with the direct solution of the Schrfdinger equation of a particle movingin afield and in aperiodic potential. A critical analysis, both qualitative and quantitative, of the experimental results usingthesetheoretical descriptions is presented.