From an extensive study of time-resolved photoluminescence in the temperature range 1.8 – 50 K on a dozen of samples of type II GaAs-AlAs superlattices, we can identify the region where the states derived from X z valleys are lower than those derived from X xy valleys. This is in agreement with a simple model involving the competition between i) X valleys splitting caused by the residual uniaxial stress in AlAs layers related to the small lattice mismatch with GaAs and ii) the difference in the confinement energies of X type states in AlAs layers related to their effective mass anisotropy. Mixing due to interface disorder of X xy and X z components into the wavefunction of these localized excitons explains the evolution of luminescence with time-delay.