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This paper analyses the general normal mixture GARCH(1,1) model which can capture time variation in both conditional skewness and kurtosis. A main focus of the paper is to provide evidence that, for modelling exchange rates, generalized two\u2010component normal mixture GARCH(1,1) models perform better than those with three or more components, and better than symmetric and skewed Student's<jats:italic>t<\/jats:italic>\u2010GARCH models. In addition to the extensive empirical results based on simulation and on historical data on three US dollar foreign exchange rates (British pound, euro and Japanese yen), we derive: expressions for the conditional and unconditional moments of all models; parameter conditions to ensure that the second and fourth conditional and unconditional moments are positive and finite; and analytic derivatives for the maximum likelihood estimation of the model parameters and standard errors of the estimates. 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