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We propose here a mathematical approach for the study of repairable systems with arbitrary distributions. The idea is to define a new type of stochastic process, called a generalized Markov renewal process (GMRP), which may describe the transition behavior of the stochastic process at non-regenerative points. In the paper an analytical method for the GMRP is put forward and the formulas are then presented for reliability analysis of repairable systems which can be described by a GMRP with finite states. A signal flow graph technique for system modeling is also summarized here. Finally, an analytical model to evaluate the reliability of a m-out-of-n:G system with general repair-time distribution is developed by means of the GMRP approach.