An EGARCH model in which the conditional distribution is heavy-tailed and skewed is proposed. The properties of the model, including unconditional moments, autocorrelations and the asymptotic distribution of the maximum likelihood estimator, are set out. Evidence for skewness in a conditional tt-distribution is found for a range of returns series, and the model is shown to give a better fit than comparable skewed-tt GARCH models in nearly all cases. A two-component model gives further gains in goodness of fit and is able to mimic the long memory pattern displayed in the autocorrelations of the absolute values.