On the basis of in-depth interviews with Arab and Israeli elites, this study delineates political styles and strategies of conflict on both sides of the Middle East dispute, with the aim of understanding their interaction effects. Three conflict orientations emerged for both Arabs and Israelis. Among Arabs, two are straight-forward: total rejection of Israel and unambiguous acceptance. All the acceptors are peripheral in their Arab identity or unusual in their contact with Israel. Through analysis of latent as well as manifest attitudes, a third, more intriguing orientation of “latent acceptance but manifest rejection” also emerges. Among Israelis, the three orientations consist of annexationism (of the occupied territories), hard bargaining, and conciliation. Although there is potential convergence between the crucial Arab “latents” and the important Israeli “hard bargainers,” their political styles and conflict strategies serve to lock the proponents of these orientations into highly competitive, intractable conflict. Exploration of the psychological needs, cultural processes, and political dynamics which give rise to these positions, together with attitudes on the issues, suggest several policies that might be effective in redirecting the process toward cooperative conflict resolution, about which all parties would feel some sense of gain.