We formulate a dynamic model of party competition with a one-dimensional policy space. Policy choices at different times are linked because parties cannot change their policies abruptly, instead, policy adjustment happens gradually. Parties are uncertain of the median’s policy preferences at the time they choose their policies. Our results relate the steady state equilibrium of the dynamic game to parties’ beliefs about voter preferences. In particular, we show that for symmetric games, the steady-state outcome is the local equilibrium of the corresponding static Wittman game.