This paper proposes a new multivariate copula regime-switching model to capture non-linear relationships in four emerging stock markets, namely Brazil, Russia, India, China (BRIC) and two developed markets (U.S. and U.K.), during five recent financial crises (the Asian crisis, the Russian crisis, the tech bust and the two episodes in Brazil). We also investigate the presence of asymmetric responses in conditional variances and correlations during these periods of negative shocks, applying the asymmetric generalized dynamic conditional correlation (AG-DCC) approach. These methods go beyond a simple analysis of correlation breakdowns, analyze the second moment dynamics of stock market returns, and enable us to overcome problems arising in the existing empirical research of financial contagion. Results provide evidence that there is an asymmetric increase in dependence among stock markets during all five crises. The jump in correlations and volatilities between stable and crisis periods supports financial contagion when crises are spread to other markets. Moreover, the differences in the magnitudes of the dependence changes show that the industry-specific tech bust appears to have a larger impact than country-specific crises. Furthermore, increases in tail dependence imply that the probability of markets crashing together is higher during periods of financial turmoil. Our findings imply that policy responses to a crisis are unlikely to prevent the spread among countries, making fewer domestic risks internationally diversifiable when it is most desirable. A further finding of this study is that the multivariate regime-switching copula model captures higher level of dependence than the AG-DCC approach, possibly due to econometric reasons.