In Chap. 4, we present ergodic theorems with explicit upper bounds for convergence rates for semi-Markov birth-death-type processes, which are regenerative processes with regeneration moments that are sequential return moments into any state, in particular, in state 0. Various upper bounds, respectively, for power and exponential moments of hitting times into state 0 are obtained using the method of test functions and recurrent relations connecting moments of hitting times for semi-Markov birth-death-type processes. Finally, ergodic theorems with explicit power and exponential upper bounds for convergence rates are given.