We provide evidence on the nature of co-movement in monthly US and UK stock returns by investigating time-varying correlations in returns since 1980. There is a marked increase in correlations between these markets around 2000, which we attribute to globalization and model with a time-varying smooth transition conditional correlation (STCC) GARCH specification. A double transition correlation model with time and US stock price volatility indicates that correlations not only increase over time but also during periods of high volatility. The STCC models perform well in comparison with constant and dynamic conditional correlation models in terms of both statistical and economic criteria, but we demonstrate that an investor will gain little from portfolio diversification across these two important markets. © 2009 John Wiley & Sons, Ltd.