We describe a scheme for constructing the characteristic equations for the macroparameters of complex heteroheneous media, the change of which is associated with microcarrier nucleation (disappearance) and growth (degradation). The approach is used to formulate models of scattered damage accumulation, where the microdefects act as the microcarriers. We construct models of damage accumulation in metallic materials, which can be used to describe the behavior of composite materials with a powder metal matrix. We also examine the question of the decay of the stiffnes of the fibrous composites during cyclic loading.