Magneto-absorption and magneto-luminescince spectra in (GaAs)m/(AlxGa1-xAs)n (type I) and (GaAs)m/(AlAs)n (type II) short period superlattices were measured in pulsed high magnetic fields up to 40T applied both parallel (B|) and perpendicular (B⊥) to the layers. Well- defined oscillatory structures were observed in type I samples with (m, n)=(6,6) and (7,5) for both field directions. For B|, the Landau level energies were calculated for both the conduction and valence band on the basis of the Kronig-Penny model, and excellent agreement was obtained with the experimental data. This result shows that the effective mass approximation is still adequate for these (m, n). In type II samples with (m, n)=(3,5) and (5,6), weak oscillations were observed only for B⊥. A very large anisotropy was observed in magneto-luminescence spectra, showing that the lowest conduction band is of the Xz character. © 1991.