We analyze the long-run relationship between the world price of crude oil and international stock markets over 1971:1–2008:3 using a cointegrated vector error correction model with additional regressors. Allowing for endogenously identified breaks in the cointegrating and error correction matrices, we find evidence for breaks after 1980:5, 1988:1, and 1999:9. There is a clear long-run relationship between these series for six OECD countries for 1971:1–1980.5 and 1988:2–1999.9, suggesting that stock market indices respond negatively to increases in the oil price in the long run. During 1980.6–1988.1, we find relationships that are not statistically significantly different from either zero or from the relationships of the previous period. The expected negative long-run relationship appears to disintegrate after 1999.9. This finding supports a conjecture of change in the relationship between real oil price and real stock prices in the last decade compared to earlier years, which may suggest the presence of several stock market bubbles and/or oil price bubbles since the turn of the century.