Stochastic models are fitted to time series of hourly precipitation amounts. These models are extensions of a form of chain-dependent process commonly fit to daily precipitation amounts. The extensions involve allowing hourly intensities to be autocorrelated and allowing the model parameters to possess diurnal cycles. These models are applied to two quite different sets of hourly precipitation data: July at Denver, Colorado, for which diurnal cycles are substantial; and January at Chico, California, for which a relatively high degree of persistence is present. The temporal aggregation properties of the hourly models (e.g., for 12-hour or daily total precipitation) are examined, and the role of the extensions in improving these properties is quantified. On this basis, it is argued that generalizations of chain-dependent processes could be competitive with, if not superior to, so-called conceptual models of the precipitation process. ¿ American Geophysical Union 1995