This paper is concerned with the dynamical problems of nonlinear thermoelasticity. Uniqueness and continuous dependence results are established for smooth admissible thermodynamic processes residing in the region of slate space where the internal energy is a convex function and the elastic material behaves as a definite conductor of heat. When the initial-displacement boundary-value problems are considered, the uniqueness and continuous dependence are established again under the weaker assumption that the thermodynamic processes reside in the strong ellipticity region in state space.