The feasibility of Bertrand undercutting with nonuniform prices is established and properties are derived for Bertrand equilibrium in nonuniform price strategies. With free entry, equilibrium entails zero-profit minimum average cost production. If there is more than one producing firm, all prices collapse to a minimum average cost uniform price. An existence condition is compared to conditions from uniform price theory. Without free entry equilibrium, prices may not collapse to a uniform price. Positive profit may occur but all firms earn equal profit and incur equal marginal cost, while consumers pay average outlay no greater than marginal cost. Copyright 1992 by The Econometric Society.