The propagation and stability of harmonically time-dependent thermoelastic plane waves of assigned frequency in the generalized thermoelasticity theory of Green and Lindsay are considered. The results are contrasted with those of the theory of Lord and Shulman. In general there is no a priori correspondence between the two theories. However, after introducing some assumptions on the constitutive coefficients α and α*, which appear in the theory of Green and Lindsay, all the corresponding results of the theory of Lord and Shulman are recovered.