This paper extends the framework of Green and Porter (1984) and Porter (1983a) to encompass the case of a cartel (OPEC) faced by a competitive fringe (non-OPEC oil producers). Estimation of a simultaneous equation switching regression model allows us to examine which market structure better characterizes the world oil market during the 1974--2004 period and to test whether switches between collusive and non-cooperative behaviour occurred. The null hypothesis that no switch occurred is rejected in favour of the alternative that both cooperative and non-cooperative behaviour was observed. We find that, although there were periods in which oil prices were measurably higher owing to collusion among OPEC members, overall OPEC has not been effective in systematically raising prices above Cournot competition levels. Our results suggest that, on average over the period of study, OPEC's behaviour is best described as Cournot competition in the face of a competitive fringe constituted by non-OPEC producers. Copyright 2011, Oxford University Press.