Nuclear war is generally believed to bring risks of destruction out of proportion to any gain that may be secured by the war, or to any loss that may be averted, except perhaps for the loss of national independence and group survival. Nuclear-armed states, however, continue to project military force outside their own territory in order to carry out rivalries for power and influence. Will these rival power projections lead to war, as they often did in the past? If not, how will they be resolved? This paper makes the case that, because of the recognized destructiveness of nuclear weapons, rivalries among major nuclear-armed states for power and influence outside their own territory are not likely to lead to central war among them, but that definite lines separating zones of exclusive security influence, such as prevailed during the Cold War, will reappear where circumstances prevent
other compromises. This conclusion does not hold in the case of nuclear powers that are centrally vulnerable to conventional attack from each other: in that case, nuclear deterrence is less likely to be stable. Where lines are established, they may facilitate rather than prevent cooperation in dealing with the next century's global problems.