Using a rotating analyzer spectroscopic ellipsometer, we have investigated the complex dielectric function of a series of ternary BexZn1-xTe thin films in the energy range between 0.7 and 6.5 eV for alloy concentrations between x=0.0 and x=0.52. After determining the alloy concentrations using x-ray diffraction and photoluminescence techniques, a standard inversion technique was used to obtain the optical constants from the measured ellipsometric spectra. Analyzing the second derivative of both the real and the imaginary parts of the dielectric constant, we have deduced the critical point parameters corresponding to the electronic transitions in the Brillouin zone. We find that the energy of the critical points with respect to Be concentration does not show any bowing effects unlike many other II–VI semiconductor ternary alloys. © 2002 American Institute of Physics.