One and two mode behaviors of surface phonon-polaritons of ternary mixed crystal (TMC) films are studied in the framework of the modified random-element-isodisplacement model and the Born-Huang approximation, based on the Maxwell's equations with the usual boundary conditions. The numerical results for the frequencies and splitting energies of the surface phonon-polaritons as functions of the composition in several II-VI and III-V compound semiconductor ternary mixed crystal films are obtained. The "two-mode'' and "one-mode'' behaviors for different types of systems are clearly shown in the curves of the splitting energies of surface phonon-polaritons. The theoretical conclusion obtained is agreement with the reported experiment results for bulk TMC systems. (c) 2008 Elsevier B. V. All rights reserved.