Hawaiian eruptions are largely random phenomena displaying no periodicity; that is, future eruptions are relatively independent of the date of the last eruption. Several simultaneous processes probably govern eruption timing so that it appears random. I have performed statistical tests for nonrandomness on the repose times between eruptions and on the sequence of event types. Statistical differences that have physical consequences exist between large and small eruptions, summit and flank eruptions, and intrusive and extrusive events. Thus, large-volume eruptions tend to be followed by longer reposes as shallow magma reservoirs refill. On Kilauea, both summit eruptions and rapid intrusions tend to cluster at times associated with other physical events on the volcano. The longest recorded reposes of both Kilauea and Mauna Loa apparently are not random phenomena, for they appear to be associated with increased activity at the other volcano. Both eruption rates and volumes are consistent with a constant but alternating magma supply to the two volcanoes and an approximately five-fold larger magma reservoir at Mauna Loa than at Kilauea. ?? 1982.