The experimental investigations of the impact loading of materials demonstrate that the process of relaxation of stresses is accompanied by the energy exchange between the macroscopic and mesoscopic levels of scales observed prior the onset of dissipation. The problem of propagation of nonstationary waves in media with relaxation is posed by taking into account the mesoscopic characteristics, such as the variance of mass velocity and the parameters determining the scales and types of mesostructures, on the basis of a self-consistent nonlocal hydrodynamic approach. It is shown that the dynamic properties of materials are determined by the thermodynamics of the macrolevel-mesolevel energy exchange. In particular, the experimental data demonstrate that the maximum cleavage strength is attained under conditions of dynamic equilibrium characterized by the minimum rate of increase in the entropy. © 2003 Plenum Publishing Corporation.