A method of analysis of spectroscopic ellipsometry (SE) measurement data is proposed forAlxGa1−xN/GaNheterostructures grown on sapphire substrates. The SE data measured at three angles of incidence, 40°, 50°, and 60°, are simultaneously fitted assuming the dielectric function to consist of a Sellmeir dispersion equation and a free-exciton absorption term. The refractive indexnand the extinction coefficientkof undopedAlxGa1−xNfilms are determined in the spectral range of 1.5–4.13 eV of photon energy. The transition energy of the free exciton, which is in excellent agreement with the reported results for GaN in a previous paper, is found to vary from 3.44 to 3.95 eV when the compositionxvaries from 0 to 0.151. The refractive indexnofAlxGa1−xNhas also been compared with those reported results. ©1998 American Institute of Physics.