Molecular beam epitaxy, using a radio frequency nitrogen plasma source, was investigated for the direct growth of GaN thin films on vicinal (001) GaAs substrates. It has been found possible to grow GaN thin films with various types of crystal structure. Cubic (001) GaN with epitaxial relationship to the GaAs substrate could be grown without GaAs nitridation and under stoichiometric N/Ga flux ratio conditions. Hexagonal mixing in the cubic GaN films occurred mainly as domains with the [0001] oriented parallel to the GaAs surface normal. Their origin was related to irregularities at the GaAs surface, produced by interaction with the N-beam. Layers which exhibited intense 17K photoluminescence with the main peak at approximately 3.42eV, presented a polycrystalline hexagonal structure with a domain width of several 100nm. These layers did not exhibit a ''yellow-band'' luminescence.