In the international edible oil markets, there is believed to be high substitutability between vegetable oils and fats produced under different conditions. In light of this, we consider the question: what is the nature of the long‐run relationships between vegetable oil prices? Long‐run co‐movements among oil prices are analysed, based on a multivariate cointegration model. The empirical finding is that most co‐movements are consistent with the predictions of market theory. Prices of oils tend to be grouped according to their different end‐uses. Some policy implications of a buffer stock scheme are discussed.