In this paper, we show that an oligopoly market where both increasing returns to scale and competition are present can nevertheless satisfy stability conditions. In a sustainable oligopoly (1) each consumer chooses the firm which proposes the price-quality schedule he prefers (2) firms earn non-negative profits (3) no new firm could attract consumers and make profits. We prove that such a sustainable oligopoly exists under rather weak assumptions. The results apply to most models of vertical or horizontal product differentiation or to models of quality differentiation due to congestion effects.