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We study the tail dependence of emerging markets in South-East Asia and we show that this tail dependence increased during the financial crisis of 2008-2010. After applying ARMA-GARCH models to individual markets, we fit various copulas to the pairs of market returns and find that in most cases tail copulas such as the t-copula and Symmetrised Joe-Clayton provide the best fit. During the crisis, nonlinear dependence measures (such as rank correlations) and the tail dependence coefficients typically increased by tenfold or even more. We apply our method to portfolio Value-at-Risk estimation and show that the copula-based Value-at-Risk performs remarkably well for South-East Asian market portfolios.