A new test for financial market contagion based on changes in extremal dependence defined as co-kurtosis and co-volatility is developed to identify the propagation mechanism of shocks across international financial markets. The proposed approach captures changes in various aspects of the asset return relationships such as crossmarket mean and skewness (co-kurtosis) as well as cross-market volatilities (covolatility). In an empirical application involving the global financial crisis of 2008-09, the results show that significant contagion effects are widespread from the US banking sector to global equity markets and banking sectors through either the co-kurtosis or the co-volatility channel, reinforcing that higher order moments matter during crises.