With the globalization of international trade and finance, the interaction between international financial markets has increased markedly. Therefore, this paper examines the nature of interaction between stock market returns and their volatility, with a particular focus on the global financial crises in 1998 and 2008 for Australia, Singapore, the UK, and the US. This study applies multivariate generalised autoregressive conditional heteroskedasticity (MGARCH) model with dummy variables for weekly data spanning from January 1992 to June 2009. Based on the results obtained from the mean return equations, we could not find any significant impact on returns arising from 1998 and 2008 global financial crises within these four markets. However, the recent crisis in 2008 increased the stock return volatilities across all of the four markets. More generally, other results show that the US stock market is the most influential market towards volatilities of smaller economies. Estimation results provide evidence of both own and cross ARCH and GARCH effects among all four markets, suggesting the existence of significant volatility and cross volatility spillovers across all four markets. The existence of higher degree time-varying co-volatility among these four markets suggests that investors will be highly unlikely to benefit from a reduction of risk if they diversify their financial portfolio with stocks within four countries only.