The dielectric function ε(ω) of polycrystalline bulk samples of the quaternary chalcopyrite semiconductors Ag1−xCuxInSe2 with x=0.0,0.2,0.4,0.6,0.8,1.0 has been determined by spectroscopic ellipsometry in the energy range from 0.5to4.7eV at room temperature. Accurate values of refractive indices n and extinction coefficients k representative of bulk materials are obtained from the data. The value of the main energy gap is very sensitive to the composition and varies from 1.225to1.009eV as x increases (Cu content). The structures observed in ε(ω) have been analyzed by fitting the numerically differentiated experimental spectrum (second derivative) to analytical line shapes. As a result, the energies corresponding to different electronic transitions have been determined as a function of the composition, and they have been identified within the electronic band structure of chalcopyrites.