Heteroepitaxial growth of single-phase nonpolar (10 (1) over bar0) m-plane AlxGa1-xN layers on m-plane sapphire substrates was investigated by metalorganic vapour phase epitaxy. Different Al/Ga gas phase ratios were used to adjust the AlN mole fraction over the entire range of composition. All m-plane AlGaN layers show an orthorhombic distortion in the wurtzite unit cell due to anisotropic in-plane strain. This distortion decreases with increasing AlN mole fraction due to a decreased anisotropic biaxial strain. The AlN mole fraction of m-plane layers and c-plane co-loaded layers estimated by X-ray diffraction is comparable. This is consistent with their comparable energy bandgaps, which were estimated from room-temperature dielectric functions. The dependence of the energy bandgap on composition indicates a bowing parameter of about 0.9 eV. The crystal-field splitting energy is found for the m-plane layers with a bowing parameter b(cf) of about -0.15 eV.