In this paper the diffusion model of the linear theory of thermoelasticity of binary mixtures is considered and the following results are obtained: the basic properties of wave numbers of the longitudinal and transverse plane waves are established. The interior boundary value problem (BVP) of steady vibration of binary mixtures of thermoelastic solids is formulated. The existence theorems of eigenoscillation frequencies (eigenfrequencies) of the BVP of steady vibrations are proved. The connection between plane waves and existence of eigenfrequencies is established.