We report here the far infrared absorption and reflection spectra of the mixed crystals ZnxCd1-xTe with small x in the temperature range of 4.2-300 K and the frequency region of 20-350 cm-1. The local and quasi-local modes induced by Zn and ZnTe in CdTe and the CdTe-like 2TA two-phonon absorption are observed. The frequencies of the modes are estimated by useing the mass-defect model combined with Green's function method. The random element isodisplacement (REI) model is used to calculated the two mode behaviors of the mixed crystals and to best fit the reflection spectra. Besides, the temperature dependence of the phonon absorption and the relaxation factor of CdTe-like and ZnTe-like modes are calculated and explained.