In this study, the authors present a novel scheme of fault-tolerant control for asynchronous sequential machines. The considered asynchronous machine is subject to permanent faults, for which the system remains in the faulty condition indefinitely after the occurrence of fault inputs. The main objective is to design an observer and a corrective controller, so that the stable-state behaviour of the closed-loop system can maintain the normal input/output behaviour despite the adversarial effect of fault inputs. It is shown that existence of such a controller depends on a certain structural redundancy of the asynchronous machine. As a case study, the authors apply the proposed control scheme to the implementation of an asynchronous Johnson counter with redundant bits. Experimental results demonstrate the applicability of the proposed fault-tolerant controller to real digital systems working in a faulty environment.