We present optical absorption experiments performed at low temperature in very high quality GaSbAlSb superlattices grown by MBE. The absorption spectra exhibit pronounced exciton peaks separated by absorption plateaus. The data are interpreted within an effective mass theory, taking into account the effect of strains induced by the 0.65 % lattice mismatch of the hosts. From the number of observed transitions, we can determine quite accurately the band offsets in this system. The crossover of the quantized states originating from the Λ and L minima of the GaSb conduction band is also discussed. © 1985.