The semimagnetic ternary semiconductor material ZnMnSe is a suitable candidate for the use in optoelectronic devices either as a spin aligner or a waveguiding layer. In our work we are studying the optical properties of Zn-1 -xMnxSe layers grown on GaAs (001) substrates by molecular beam epitaxy. We present the complex dielectric function obtained by variable-angle spectroscopic ellipsometry in the photon energy range from 0.75 to 4.5 eV Between 0.75 and 3.3 eV the experimental data are fitted with a critical-point parametric model. The energies of E-0, E-0 +Delta(0), E-1 and E-1 + Delta(1) critical points are given for ZnSe and Zn0.87Mn0.13Se. (C) 2003 Elsevier B.V. All rights reserved.