The focus of this article is the management of arguments between Israeli Jews and Palestinian Arabs. Israelis and Palestinians are 2 groups that have been in severe conflict about land, culture, history, and national rights. In this study we draw on the traditions of conversation analysis, logic, and rhetoric to explain how participants used arguments to manage certain dilemmas and problem. The data were group encounters between Israeli Jews and Palestinians. This analysis highlights the role of symbolic ethnocentrism m argument, the problem of grounded premises that forestall progress, and various argumentative strategies (e.g., question asking collaborative argument, limited topical space) that serve the rhetorical goals of the participants.