Model matching for an asynchronous sequential machine is to design a feedback controller that compensates the closed-loop system so that it can match the behavior of a reference model. The objective of this paper is to address the model matching problem for a composite asynchronous sequential machine. Two input/state asynchronous machines in cascade connection form a composite machine, where the output of the front machine is transmitted as the input to the rear machine. Given a desired model, we present the existence condition and design procedure for an appropriate corrective controller that achieves model matching. An illustrative example is provided for verifying the applicability of the proposed scheme.