We assess the extent of integration between stock markets during stressful periods using the concept of copulas. Our methodology consists of fitting copulas to simultaneous exceedances of high thresholds, and computing copula-based measures of interdependence and contagion. Using 21 pairs of emerging stock markets daily returns, we investigate if dependence increases with crisis, and analyse the chances of both markets crashing together. Dependence at joint positive and negative extreme returns levels may differ. This type of asymmetry is captured by the upper and lower tail dependence coefficients. Propagation of crisis may be faster in one direction, and this feature is captured by asymmetric copulas. Copyright (c) 2005 John Wiley & Sons, Ltd.