Molecular beam epitaxy using a radio-frequency nitrogen plasma source was applied for the growth of GaN films on (I 11) and (00 1) faces of GaAs wafers. The structural assessment by TEM of the grown films revealed that hexagonal phase with columnar morphology has formed on (I 11) substrates. In contrast to that, depending on the actual deposition parameters, both hexagonal and cubic polytype could be grown on (001) face of GaAs. Nitrogen rich conditions before and during deposition favoured the hexagonal phase, while stoichiometric N/Ga ratio and the lack of substrate nitridation resulted in the cubic structure. Several epitaxial orientation relationships for the individual cases have been determined and discussed.