We analyze two-part tariffs in oligopoly, where each firm commits to a certain quantity. The model is an extension of the one introduced in Har (2001). We show that their main results are reversed when the model is extended from one to two types of consumers. In particular, we find that price per unit can exceed marginal costs, and the fixed fee can be below costs. We also show that two-part tariffs may collapse, because each firm would rather commit to a traditional Cournot price system (zero fixed fee). Finally, some numerical examples illustrate that both firms serving both types of consumers can be an equilibrium outcome in duopoly in cases where the monopolist would serve only one type of consumers