The temperature and concentration dependences of the elastic moduli and the thermal linear expansion coefficient of ZrzNb1 – zCxNy solid solutions containing from 3 to 8 at % of structural vacancies in a nonmetallic sublattice have been found. The temperature dependences of the Debye temperature ΘD(T) have been calculated using the elastic data and the data on the heat capacity. It has been shown, using carbide NbC0.97 as an example, that the ΘD(T) dependences found from the elastic properties and the heat capacity coincide in the temperature range ~220–300 K. By analogy with the niobium carbide, the heat capacity Cp(300) of ZrzNb1 – zCxNy solid solutions of various compositions is calculated based on the values of ΘD(300) determined from the elastic properties.