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R. F. Engle's autoregressive conditional heteroskedastic model is extended to permit parametric specifications for conditional dependence beyond the mean and variance. The suggestion is to model the conditional density with a small number of parameters, and then model these parameters as functions of the conditioning information. This method is applied to two data sets. The first application is to the monthly excess holding yield on U.S. Treasury securities, where the conditional density used is a Student's t distribution. The second application is to the U.S. Dollar/Swiss Franc exchange rate, using a new skewed Student t conditional distribution. Copyright 1994 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.