The problem of combined translational and internal relaxation of sound waves in polyatomic gases is studied using the 17‐moment approximation. When applied to the sound problem, the moment equations, which are valid for any number of internal degrees of freedom, yield a generalized complex matrix eigenvalue equation which is solved numerically for the absorption coefficient and propagation speed as a function of the rarefaction parameter (the approximate ratio of collision frequency to sound frequency). The physical parameters in the equations are the self‐diffusion coefficient (assumed the same for each internal mode), the internal relaxation times, and the internal specific heats. Our solutions for the combined absorption for the case of a single internal mode are compared to those obtained assuming the total absorption is the sum of that due to the translational and internal effects separately, and to that obtained by using the combination rule of Greenspan. Comparison is also made between the combined dispersion calculated by the 17‐moment method and the Greenspan rule. In addition, absorption curves are calculated for the case of two internal degrees of freedom for various combinations of internal collision numbers. When applied to rotational relaxation inN2our theory yields, for a rotational collision number of 5.26, good agreement with experiment over the range of values of the rarefaction parameter for which a continuum theory is expected to be valid.