The dielectric functions of the wide-bandgap semiconductors GaN and AlxGa1-xN (hexagonal phase on c-sapphire) are determined directly for the first time in the spectral range 3-25 eV using an ellipsometry set-up operating with synchrotron radiation at the Berlin electron storage ring BESSY I. The compositional dependence of the transition energies of interband-critical points located in the vacuum ultraviolet spectral region, which are not accessible to ellipsometers using conventional light sources, was determined for 0 less than or equal to x less than or equal to 1. Additional measurements with a visible-UV ellipsometer have been performed to determine precisely the fundamental gap E-0. A systematic parabolic shift of E-0 towards higher energies was found with increasing Al content while higher interband transitions show a linear shift. Differences in morphological properties of a MBE-and a MOCVD-grown GaN sample and their influence on the measured dielectric function are discussed.