GaN films epitaxially-grown on M-sapphire may have different orientations, either nonpolar and semipolar. In this paper, the different epitaxial relationships are investigated in details thanks to transmission electron microscopy. It is shown that these relationships drastically depend on the nitridation conditions. Mechanisms explaining the different epitaxial relationships are proposed. These mechanisms take into account the formation of a nitridation layer, the lattice mismatches between the growing films, and the substrate, and the surface energies. It is, moreover, shown that the difference of symmetries between the M-sapphire surface and the epitaxial films leads to the formation of growth twins for the (10 (1) over bar0) and (10 (1) over bar(3) over bar) orientations. (C) 2010 American Institute of Physics. [doi:10.1063/1.3514095]