Using data from two stations in the MAP3S acid precipitation monitoring network, some aspects of the marked point process of rainfall events are investigated and are used to illustrate some potentially useful data analytic techniques. We find no statistically significant evidence against a Poisson process model of storm arrivals, observed with a dead time corresponding to event duration. In particular, we look at the relation between amounts and the history of the process of events and the relation between events at two different stations. Events that occur close to previous events tend to have smaller than average precipitation amounts. We discuss some implications for parametric models of precipitation processes.