A flexible multivariate model of a time-varying joint distribution of asset returns is developed which allows for regime switching and a joint skew-normal distribution. A suite of tests for linear and nonlinear financial market contagion is developed within the framework. The model is illustrated through an application to contagion between US and European equity markets during the Global Financial Crisis. The results show that correlation contagion dominates coskewness contagion, but that coskewness contagion is significant for Greece. A flight to safety to the US is also evident in the significance of breaks in the skewness parameter in the crisis regime. Comparison to the Asian crisis shows that similar patterns emerge, with a flight to safety to Japan, and Malaysia affected by coskewnes contagion with Hong Kong.