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The phase type distribution gives the time till absorption in a finite state space Markov chain with one absorbing state (or a set of absorbing states). The sojourn time and transitions among the states are governed by a semi-Markov process with sojourn time exponentially distributed. Thus it is generated by a Markov chain of order 1. Now consider a second order Markov chain on a finite state space and an absorbing state. What will be the nature of the PH distribution generated by this second order Markov chain. In particular, how does the mean absorption time between the two compare. Some applications will be indicated.