We report on results of low-temperature photoluminescence measurements performed on GaN films, grown by molecular beam epitaxy (MBE) on sapphire substrates. The GaN films are either Mg doped (p-type) or consist of a Mg-doped layer on top of a Si doped GaN layer (n-type). In the p-doped samples, the sharpness of the donor-acceptor-pair transition is striking, three phonon replicas are clearly resolved. A transition band occurs around 3.4 eV, which becomes dominant for samples with an np-layer structure. The position and the composition of the near band edge transitions are influenced by the growth of the buffer layers. Depending on the growth conditions a transition at 3.51 eV can be observed.