We analyze the evolution of duopolists' prices and market shares in an infinite-period market with consumer switching costs, in which in every period new consumers arrive and a fraction of old consumers leaves. We show prices (and profits) are higher than without switching costs, and that this result does not depend importantly on our specific assumptions. We show switching costs make the market more attractive to a new entrant, even though an entrant must overcome the disadvantage that a large fraction of the market is already committed to the incumbent's product. We also examine the effects of market growth.