Under the assumption of single peaked preferences, the majority rule equilibrium considered as a correspondence from the voters' preference is shown to be continuous. We also complement the work of Fishburn [6], who first presented a general location theorem for majority rule equilibriums, by dropping the assumptions that the alternative set is finite and that voters' preferences are strict partial orders. SINCE THE WORK of Black [3] on simple majorities and single-peaked preferences, much work has been done in deriving conditions for which some state achieves a majority over all other states. It is also well known that the equilibrium in many cases is the median of the distribution of most preferred states of the voters. (See [3, pp. 14-18].) We present here a result concerning the continuity of the majority rule equilibria. Specifically, we show that in the case of single-peaked preferences, the majority rule equilibrium depends only on the peaks of the voters' preferences and not on the transitivity properties of these preferences. We then show that the equilibrium, viewed as a correspondence of these peaks, is continuous (i.e., both upper and lower semicontinuous). This result is especially important when one tries to prove the existence of an equilibrium in a political-economic system. Most existence theorems are based on fixed point theorems which require at least upper semicontinuity of the correspondences being studied. The theorem proved here shows that the majority rule equilibrium is continuous in voters' peaks. If these are in turn continuous functions of other parameters such as prices, then our result might aid one in deriving general existence theorems for social equilibria. (See [3 or 4].) The only related work seems to be that of Kelly [10] who investigates the existence of a continuous numerical representation of the social preference relation generated by majority rule. He shows that one cannot expect continuity even if the social preference relation has other properties, such as transitivity. Specifically, he presents a case in which a majority of voters are indifferent between two points. In a neighborhood of one of these points, this majority rules between points in the neighborhood and the other point, but a minority (since the majority is indifferent) rules between the two given points. Hence one cannot expect continuity of the