In this paper, the censoring technique is used to deal with block-structured Markov renewal processes. Two probabilistic measures the R-and G-measures are defined and a censoring invariant property for the R- and G-measures is obtained The RG-factorization for the ransition probability matrix is dcrivcd based on the Wiener-Hopf type the transition probability matrix consists of two sequences of matrices one is refered to as the probability matrix consists of two sequences of matrices one is referred to as the boundary sequence and the other the repeating sequence Thw, RG-facteiation of the double transformations for the reqeating matrix sequence and four matrix inequalities of the double transformations for the boundary matrix sequence are given.