We propose a new approach to the study of financial contagion and contagion channels in the forex market by using a dynamic mixture copula-extreme value theory (DMC-EVT) model. This method allows us to elucidate the complex and dynamic dependence between forex markets. By analyzing 39 currencies that are actively traded on the forex market during the period 2005-2009, our empirical study shows that the DMC-EVT model outperforms the alternative copula models. Furthermore, we confirm the existence of financial contagion in the forex market during the 2007-2009 global financial crisis, and find that wealth constraints are the contagion channel during the crisis. Our results provide important insights on portfolio and risk management.