Abstract The law of one price states that prices of homogenous commodities, defined in a common currency, are equal throughout the world. It implies cointegration of prices. In the present study, the law was tested for imports of soft sawnwood to the United Kingdom from Finland, Sweden, Canada, and Russia using the concept of cointegration. The data are quarterly and cover the period 1978-1992. The study used the multivariate cointegration method of Johansen instead of the bivariate method commonly used in earlier studies. The existence of the law was tested simultaneously for all four import prices and separately for pairs of prices. The results do not support the "law" but instead indicate the existence of differences over the long run between different suppliers' sawnwood prices. This suggests that imperfect competition models should be used in explaining and forecasting UK sawnwood imports. The results also raise an important issue concerning testing for competition in forest products markets, which is not usually done in connection with the modeling of markets. For. Sci. 44(1):17-23.