In distributed multinode data processing systems, mechanisms are employed to insure that the nodes are continually informed about the liveness of the other nodes within node groups in the network and across networks. The method of the present invention employs the concept of node stability which it uses to provide indications of membership in a previous stable group as part of messages transmitted in a protocol for forming, maintaining and dissolving node groupings in such a way as to assure that all of the nodes in the group have a consistent indication of liveness status for all of the nodes within any given group of nodes.