The problem of model matching for asynchronous sequential machines consists of finding a feedback controller for a given open-loop machine so that the resulting closed-loop machine matches a desired model. In this paper, the control objective is extended to model matching inclusion in which the behavior of the closed-loop system should be contained in that of the model. The supremal controllable sub-model is characterized as an asynchronous machine with the largest behavior set contained in a given model that can be matched by the closed-loop machine via state feedback control. An effective computational algorithm is developed and an example is provided for illustration. (c) 2011 Elsevier Ltd. All rights reserved.