The behavior of two groups of nations, superpowers and regional powers, engaged in an arms race represented as a differential game are studied. The various nations are assumed to arm themselves according to a balance of power, the policemen, or the second attack rationale. The regional nations are assumed to control the disposition of strategic resources desired by the superpowers. To obtain these, the superpowers provide assistance to the regional nations. The optimal trajectory corresponding to the above three rationales is computed, and the stability of the trajectory is studied. After a change in the international situation, the regional nations may alter the distribution of the material to the various nations. The effect of this on the stability of the resulting optimal trajectory is investigated.