This paper provides some insight into the asymmetric effects of stock market volatility transmission using weekly stock market return data (January 1992-June 2010) of four countries, namely, Australia, Singapore, the United Kingdom and the United States within a MGARCH (multivariate generalised autoregressive conditional heteroskedasticity) framework. Our results indicate that negative shocks in each market play a more important role in increasing both volatility and covolatilities than positive shocks. In addition, as expected, we identified that all markets (particularly Australia and Singapore) exhibit significant positive mean and volatility spillovers from the US stock market returns, but not the other way around.