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A deadlock avoidance method for flexible manufacturing systems with both free choices and multiple resource requests allowed in part routing is presented. Based on a digraph model of the system, the method classifies whether moving a part to its next step is safe, unsafe, or undetermined. An undetermined part movement is further analyzed using a very efficient system simulation, which attempts to empty the system virtually to determine whether the move is safe. This classification algorithm is shown to be polynomial in complexity. To avoid deadlocks, only safe part movements should be allowed to proceed. An example is provided to illustrate how the method can be applied.