I first show that if there are more than two potential candidates in the Hotelling- Downs model of the simultaneous choice of positions by politicians then an equilibrium fails to exist in a wide range of situations. Subsequently I study a temporal model in which candidates are free to act whenever they wish. For the case of three potential candidates I nd that in every equilibrium exactly one candidate enters. There is always an equilibrium in which the position cho- sen by the entrant is the median: the only other possibility is that the position chosen is far from the median.