The concept of logical consistency of belief among a group of computational agents that are able to reason nonmonotonically is defined. An algorithm for truth maintenance is then provided that guarantees local consistency for each agent and global consistency for data shared by the agents. The algorithm is shown to be complete, in the sense that if a consistent state exists, the algorithm will either find it or report failure. The implications and limitations of this algorithm for cooperating agents are discussed, and several extensions are described. The algorithm has been implemented in the RAD distributed expert system shell.>