Abstract : A class of bargaining sets, including the bargaining set M(sub 1)(sup i) and the kernel, is treated with regard to studying the tendency to reach stability from unstable points. A known discrete procedure is extended, and these results are applied to derive global stability properties for the solutions of certain differential equations. These differential equations are given in terms of the demand functions which define the bargaining sets, and the set of critical points is precisely the bargaining set in question.