We have systematically studied (GaAs) m(AlAs) n short period superlattices (SPS) grown by MBE with various values for m and n (2 ≤ m,n ≤ 73) by means of picosecond photoluminescence and photoluminescence excitation spectroscopy. The SPS with different m,n can be classified according to their excitation spectra and luminescence recombination times into two groups, namely direct gap like (type 1) and indirect gap like (type 2) structures. The recombination times of the type 1 SPS decreases continuously with decreasing GaAs and AlAs layer thickness from about 510 ps for a (GaAs)72(AlAs)63 SPS to about 250 ps for a (GaAs)3(AlAs)1 SPS. The luminescence decay in the type 2 samples is much slower and is in the order of μs for a (GaAs)7(AlAs)7 SPS at low temperatures. In addition we observe a high energy luminescence component in type 2 samples, which decays within our time resolution of 20 ps. A temperature induced type 2 — type 1 crossing is observed for a (GaAs)2(AlAs)2 SPS.