Abstract: Surface phonon-polaritons in slabs of polar ternary mixed crystals are investigated with the modified random-element-isodisplacement model and the Born-Huang approximation,based on Maxwell’s equations with the usual boundary conditions.The numerical results of the surface phonon-polariton frequencies as functions of the wave-vector and thickness for slabs of ternary mixed crystals AlxGa1-xAs,ZnxCd1-xS,and GaxIn1-xN are obtained and discussed.It is shown that there are four branches of surface phonon-polaritons in slab systems.The "two-mode" and "one-mode" behaviors of surface phonon-polaritons are also shown in their dispersion curves.

Key words: surface phonon-polaritons, ternary mixed crystals, slab of semiconductor