This article estimates autoregressive conditionally heteroscedastic (ARCH) and generalized ARCH (GARCH) models for five foreign currencies, using 10 years of daily data, a variety of ARCH and GARCH specifications, a number of nonnormal error densities, and a comprehensive set of diagnostic checks. It finds that ARCH and GARCH models can usually remove all heteroscedasticity in price changes in all five currencies. Goodness-of-fit diagnostics indicate that exponential GARCH with certain nonnormal distributions fits the Canadian dollar extremely well and the Swiss franc and the deutsche mark reasonably well. Only one nonnormal distribution fits the Japanese yen reasonably well. None fit the British pound. © 1989 American Statistical Association.