This paper is a sequel to "On the Stability of the Competitive Equilibrium, I," by K. J. Arrow and L. Hurwicz. It extends the results of "I" in several directions. In particular, it provides a proof of stability in the large (and not merely locally) when all goods are gross substitutes; this result is found to be valid for processes where the price adjustment rate is a continuous sign-preserving, but not necessarily proportionate, function of excess demand. The paper deals both with systems where one of the commodities plays the role of numeraire and with systems where all commodities are treated symmetrically.