This paper analyses returns and volatility linkages between the South African (SA) equity market and the world major equity markets using daily data for the period 199-2007. Also analysed is the nature of volatility, the long term trend of volatility and the risk-premium hypothesis. The univariate GARCH and multivariate Vector Autoregressive models are used. Results show that both returns and volatility linkages exist between the SA and the major world stock markets, with Australia, China and the US showing most influence on SA returns and volatility. Volatility was found to be inherently asymmetric but reasonably stable over time in all the stock markets studied, and no significant evidence was found in support of the risk-premium hypothesis.