Joint tests of contagion are derived which are designed to have power where contagion operates simultaneously through coskewness, cokurtosis and covolatility. Finite sample properties of the new tests are evaluated and compared with existing tests of contagion that focus on a single channel. Applying the tests to daily Eurozone equity returns from 2005 to 2014 shows that contagion operates through higher order moment channels during the GFC and the European debt crisis, which are not necessarily detected by traditional tests based on correlations.