In this article we study the classical solutions of the mixed initial-boundary value problem in the linear dynamic theory of anisotropic thermoelasticity. Conditions are established to ensure that the classical solution is either Hölder or logarithmic stable. These two forms of continuous dependence are pertinent to certain problems which require a numerical solution. The method adopted is an extension of the familiar energy arguments of continuum mechanics. Some uniqueness theorems are also presented. © 1977 Springer-Verlag.