It is demonstrated here, that luminescence experiments provide a direct and reliable tool to investigate the properties of donor bands in very high magnetic fields. The change of their binding energy, wavefunction and overlap is much more directly reflected in these experiments than in transport measurements, as e. g. Hall effect experiments, where only the magnetic freezeout of charge carriers can be observed. Undoped p-type GaSb exhibits acceptors with ionization energies between 13 and 100 meV. Low temperature luminescence spectra are reported involving transitions to the different acceptors. The excitation intensity dependence and magnetic field dependence up to 100 kG of these spectra were investigated. With increasing magnetic field the acceptor lines shift to higher energies and split by about 4 meV at 100 kG. The shift is nearly independent of the acceptor ionization energy and depends only on the concentration of the impurities. With increasing excitation the lines shift to higher energies. The A, B, C, E and F lines are identified to be donor-acceptor transitions. The splitting of the lines in a magnetic field is discussed in terms of spin-splitting of the donors and a relocalization of the donor-impurity band which has merged with conduction band tails. This effect is known to cause the magnetic freezeout of charge carriers in transport experiments. The magnetic field shift of the dominating low energy component of the recombination lines is explained by these two effects and by Larsen's theory of donor levels in a magnetic field