It is desirable in many applications, that a set of cooperating processes do not loose their coordination due to failures. This paper presents a fault-tolerant protocol for a network of processors, which form a logical ring on a physical broadcast medium. The presented protocol makes possible for a set of processes to reestablish their normal operation after transient or permanent process failure or transient communication failures. The protocol is described, model for the system is developed, and in the framework of this model it is proved, that the system reaches a stable and correct configuration in finitely many steps after failure.