It was recently shown that if a contact of two purely elastic bodies with no sliding is subjected to oscillations in normal and tangential directions, a kind of damping occurs due to relaxation of tangential stress in areas of intermittent contact, despite the absence of sliding and corresponding frictional work. In the present paper we show that the same mechanism acts in contacts with superimposed normal and torsional oscillations. A closed-form solution for the torsional and combined (torsional/tangential) relaxation dissipation for a contact of arbitrary bodies of revolution is presented.