In Chap. 11 , we present ergodic theorems with explicit upper bounds for convergence rates for multi-alternating regenerative processes with semi-Markov modulation. These processes generalize naturally both regenerative and semi-Markov processes. We introduce multi-alternating regenerative processes modulated by semi-Markov processes and give renewal-type equations for distributions of multi-alternating regenerative processes and relations connecting their distributions and the distributions of accompanying Markov processes for modulating semi-Markov processes. We give two series of ergodic theorems with explicit power and exponential upper bounds for convergence rates for multi-alternating regenerative processes modulated by semi-Markov processes with atoms and for multi-alternating regenerative processes modulated by semi-Markov processes admitting artificial regeneration.