A model of the organization of the international wheat market is presented (a) to explain historical competitive behaviour in the market and (b) as a framework for analysing the likely effects of changes in market conditions on competitive behaviour. In the model the market is segmented into three interdependent sub-markets. The hard wheat sub-market is characterized by a co-operative duopoly model with Canada as the price leader, with the United States as the usually silent partner, and with a fringe of competitors. The soft wheat and durum wheat sub-markets are characterized by oligopoly models based on imperfect collusion between the three main respective sellers, and with a fringe of competitors. It is found that prices (particularly of hard wheats) are more stable and higher than would be prices formed under free market conditions and there is a greater emphasis on the use of non-price competition. The model indicates the importance of domestic agricultural policies in assuring continued stability in the market.