Arguments are presented to show that the internal energy per molecule in a macroscopically small volume element of an infinite liquid should remain constant, in first approximation, during a sudden fluctuation in liquid structure at constant density and temperature. This result is shown to be consistent with a formulation of nonequilibrium thermodynamics in which the departures of structural parameters from their local equilibrium values appear as thermodynamic variables and in which there is no relaxing structural specific heat. However, it is shown that such a relaxing specific heat must appear in the treatment of variables which give the populations of internal states. Consistent with this fact a new theory of thermal relaxation, which includes inertial effects, is formulated. It is shown, on plausible assumptions, that one can calculate all the rate constants and relaxation times introduced to describe inertial effects, as well as the thermodynamic forces.