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A Petri net approach to determining the conditions for stability of a re-entrantsystem with buffer priority scheduling policy is described in this paper. The concept of bufferboundedness based on the dynamic behavior of the markings in the system model is emphasized.The method is used to demonstrate the stability of the first buffer first served (FBFS) and thelast buffer first served (LBFS) scheduling policies. Finally a sufficient condition for instability ofsystems with a positive feedback loop (PFL) is established, and an example is given.