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An asynchronous sequential network is an interconnection of several asynchronous sequential circuits. Asynchronous networks are classified according to the relative time delay of the individual circuit's feedback signals and input signals. They are also classified by the manner in which the circuits interact. In addition, another network model uses duplicate paths for the feedback signals and the input signals of a circuit where the duplicate paths have differing delays. The partition theory of Hartmanis and Stearns  is used for characterizing some of the network types in a manner analogous to the characterization of synchronous sequential networks. The special case where each circuit in the network has only two states is equivalent to specifying a state assignment for the overall network and this leads to a characterization of some state assignments for asynchronous circuits. In particular, any arbitrary state assignment for the network which has duplicate paths and delays is shown to be free of critical races, and another network model leads to a variation of the minimum transition-time state assignments which in certain cases may require fewer state variables.