We develop a model of alternating price competition between firms selling differentiated products to nonhomogeneous consumers. Subgame perfect equilibria exist that support quite collusive prices even though each firm's price depends only upon its rival's current price. We find two types of equilibria. One, which we call "disciplined," arise when products are close substitutes. The other, which we call "spontaneous," emerge when products are more differentiated. In disciplined equilibria the steady-state price is enforced by the implicit threat to respond to a price cut with further price cutting. In spontaneous equilibria no such threat is needed. Consumers in the smaller market tend to pay a higher price, as do consumers in the market served by the more efficient firm. The price supported by a disciplined equilibrium is greater the less differentiated are the products.