Necessary and sufficient conditions for weak convergence of first-rareevent times for semi-Markov processes, obtained in the first part of this paper Introduction In the first part of the present paper We use all notations and conditions introduced in the first part of the present paper as well as continue numbering of sections, theorems and lemmas began there. First-rare-event times for semi-Markov processes considered in the first part of the present paper reduce to random geometric sums in the case of degenerated imbedded Markov chain. In this way, our results are connected with asymptotical results for geometric sums. Here, we would like first to mention originating papers b
