Why do states with few or no nuclear weapons challenge and resist opponents with superior nuclear capabilities? International relations theory and common sense suggest that these instances should be rare. However, conflict in these asymmetric nuclear balances, what I call nuclear primacy, occurs very frequently. I argue that such conflict occurs because nuclear primacy creates the opportunity for the inferior side to use limited force to redress political grievances. The argument is therefore a story of motive and opportunity. On the motive side, states are most likely to challenge or resist rivals with superior nuclear forces when they believe there is a threat to their core interests. On the opportunity side, nuclear primacy permits conflict because the low threat to the strong side's nuclear arsenal reduces the dangers for deliberate and accidental nuclear use. The dangers of pressing too hard and inviting nuclear retaliation will tend to constrain the amount of force that the weak side will utilize. As such, though conflict will occur quite frequently in nuclear primacy, it will tend to remain limited. The inferior side is most likely to press the issue to war when it has outside support that can constrain the nuclear superior side or it is directly attacked. I test the argument by examining conflict in nuclear primacy from 1945-2000. Specifically, I examined data on all states' nuclear arsenals from 1945-2000 and found that nuclear primacy permits frequent, low-level conflict. I next examined a series of historical case studies in nuclear primacy. These included periods of conflict and no conflict as well as confrontations that did and did not escalate to war. Consistent with my argument, conflict was most likely to occur when the nuclear inferior side faced a challenge to its core interests. During the confrontations the inferior side proceeded in a cautious manner, testing and probing the strong side's reaction to attain a favorable political settlement.