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This paper presents a method for modeling the operation of the frame synchronization algorithms of the several levels of a synchronous time division multiplex hierarchy as a Markov chain. A method, discussed elsewhere by one of the authors, is used to drastically reduce the number of states in the Markov chain and make a numerical calculation of the mean first passage times possible. The mean reframing times as a function of appropriate parameters are determined for three examples, with one approaching the complexity of a practical system. A determination of the same quantities by methods unrelated to the proposed approach gives results which are in excellent agreement.