The problem of model matching for finite-state asynchronous sequential machines is examined. In particular, the considered asynchronous machine may receive uncontrollable external inputs, i.e., of which values the controller cannot change or disable. For realizing model matching with a reference model, the asynchronous machine must have additional reachability to deal with transitions by uncontrollable inputs. Necessary and sufficient conditions for the existence of an appropriate controller are given in terms of a reachability relation between the machine and the model. A characterization of feasible control laws is derived and algorithms for their design are outlined.