Gains from international portfolio diversification may be limited if national stock markets are cointegrated. In addition, the implied Granger-causality would be consistent with inefficiency. This possibility is discussed and the relationships between stock market indices of the US, the UK, Japan, West Germany and the Netherlands are investigated using bivariate and multivariate techniques. Contrary to some earlier empirical results, with the exception of the UK and Japan, there is no convincing evidence that international stock markets were cointegrated in the period following the abolition of exchange controls in the UK.