We examine whether a significant long-run relationship between the US, UK and Australian stock market prices exist and whether this relationship is temporally stable, based on the use of cointegration methodology as applied to the period 1984 to 2001. We find a stationary long-run relationship between the UK and the US, but not between the Australian and US, and Australian and UK, markets. Our results further reveal that the UK-US relationship was impacted by two structural shocks - the October 1987 stock market crash and the 1993-1994 US bond market crash. This relationship was stable during the period before the October 1987 crash and remained to be so after this period until it was disrupted by the 1993-1994 US bond market crash. During the period after 1994 up to 2001, this relationship between the UK and US markets, however, ceased to exist. Thus, for investors with UK and US stocks in their portfolios, there was no need for re-balancing of their portfolio during the periods of 1984 to 1993 but this had to be done after 1994.