The model matching problem of asynchronous sequential machines is to design a corrective controller such that the stable-state behavior of the closed-loop system matches that of a prescribed model. In this paper, we address model matching when the external input set consists of controllable inputs and uncontrollable ones. Like in the frame of supervisory control of Discrete-Event Systems (DES), uncontrollable inputs cannot be disabled and must be transmitted to the plant without any change. We postulate necessary and sufficient conditions for the existence of a corrective controller that solves model matching despite the influence of uncontrollable events. Whenever a controller exists, the algorithm for its design is outlined. To illustrate the physical meaning of the proposed problem, the closed-loop system of an asynchronous machine with the proposed control scheme is implemented in VHDL code.