In Chapter 3, we introduce a model of perturbed semi-Markov processes, formulate basic perturbation conditions, describe a one-step time-space screening procedure of phase space reduction for perturbed semi-Markov processes, introduce hitting times, and prove an invariant property of them with respect to the procedure of phase space reduction. We, also, present algorithms for re-calculation of asymptotic expansions for transition characteristics of nonlinearly perturbed semi-Markov processes with reduced phase spaces and algorithms for sequential reduction of phase space for semi-Markov processes and construction of Laurent asymptotic expansions, without and with explicit upper bounds for remainders, for power moment of hitting times. © 2017, The Author(s).