We report pseudodielectric functions [epsilon] of the quaternary semiconductor alloys CuAlxIn1-xSe2. Measurements were done in polycrystalline samples from 0.7 to 5.1 eV at room temperature by spectral ellipsometry. Accurate values of refractive indices n and extinction coefficients k representative of the bulk materials are reported. The dependence on composition of the reflectivity at normal incidence R(x) at the He-Ne laser wavelength lambda =1.523 mum provides an optical method to determine the composition of these alloys. The structures observed in [epsilon] are analyzed by fitting the numerically differentiated spectra of d(2)[epsilon](omega)/d omega (2) to analytic line shapes. The obtained energies are related to given interband transitions by taking into account the electronic band structures of the ternary end-point compounds. (C) 2000 American Institute of Physics. [S0021-8979(00)00923-3].