This study develops a dynamic model of the rivalry process, explicitly connecting the conflicts that form rivalries. The model demonstrates how these conflicts combine to form an especially conflict-prone relationship. Using numerical simulations of the model, I deduce and test a hypothesis connecting dyadic conflict and rivalry termination. High-concentration conflicts increase the probability of rivalry termination by causing a sharp and sustained drop in public support for future military action. Dyadic conflict between rivals can bring peace, under the right circumstances. The article concludes with a discussion of the model's implications for policymakers seeking to limit international violence.