The paper is concerned with an application of non-zero-snm differential games of macroeconomic system illustrated in the balance-of-payments adjustment problem between the two countries. The optimal policy solutions of the game model with quadratic performance index are obtained by means of the properties of the pseudo-inverse matrix. Sequentially, necessary and sufficient conditions for the existence of min-min game solutions, which correspond to min—max game solutions, are presented as one of the principal results of the present paper.