We determined the dielectric function of the alloy system (AlxGa1−x)2O3 by spectroscopic ellipsometry in the wide spectral range from 0.5 eV to 8.5 eV and for Al contents ranging from x = 0.11 to x = 0.55. For the composition range x<0.4, we observe single phase material in the b-modification and for larger Al content also the occurrence of γ-(Al,Ga)2O3. We derived spectra of the refractive index and the absorption coefficient as well as energy parameters of electronic bandband transitions by model analysis of the dielectric function. The dependence of the dielectric functions lineshape and the energy parameters on x is highly continuous, reflecting theoretical expectations. The data presented here provide a basis for a deeper understanding of the electronic properties of this material system and may be useful for device engineering.