Epitaxial growth of AlInGaN/GaN heterostructures on sapphire substrates was achieved by plasma-induced molecular beam epitaxy. Different alloy compositions were obtained by varying the growth temperature with constant Al, In, Ga and N fluxes. The In content in the alloy, measured by Rutherford backscattering spectroscopy, increased from 0.4% to 14.5% when the substrate temperature was decreased from 775 degreesC to 665 degreesC. X-ray reciprocal space maps of asymmetric AlInGaN (2.05) reflexes were used to measure the lattice constants and to verify the lattice match between the quaternary alloy and the GaN buffer layers.