The dielectric functions of GeSn and GeSiSn alloys were measured in the 1-6 eV energy range using spectroscopic ellipsometry. The contributions from the E-1, E-1 + Delta(1), E-0', E-2, and E-1' critical points in the joint density of electronic states were enhanced by computing numerical second derivatives of the measured dielectric function, and the resulting lineshapes were fitted with model expressions from which the critical point energies, amplitudes, broadenings, and phases were determined. A detailed analysis of the compositional dependence of the different transition energies is presented. By describing this dependence in terms of quadratic polynomials, the bowing parameter (quadratic coefficient) for each transition is determined. It is shown that the bowing parameters in the ternary alloy follow a distinct chemical trend, in which the ternary is well described in terms of bowing parameters for the underlying binary alloys, and these bowing parameters increase as a function of the size and electronegativity mismatch of the alloy constituents. (C) 2015 Elsevier Ltd. All rights reserved.