The problem of asymptotic consolidation has been considered in a large number of investigations; they can be divided into three directions. In [I-3] one develops an analytic approach, connected with the investigation of the behavior of the solutions of the Markov renewal equations, which operates effectively at the analysis of homogeneous Markov processes (MP) and semi-Markov processes (SMP). In [4, 5], by direct probabilistic methods one has obtained a rapproachement of the characteristics of a consoliated process and of a process of the SMP type for processes with a discrete set of states. In [6-9] one has developed a new approach to the problems of asymptotic consolidation, making use of a special class of processes, viz., switching processes, which is effectively applied in [~0-12] to the analysis of both homogeneous and nonhomogeneous MP and SMP.