Recently obtained information on rainfall maxima on the island of La Réunion, about 400 mi. east of Madagascar, established new records for durations from 9 hr. to 8 days. Some of the previous record values for 15 to 24 hr. were exceeded also by Taiwan rainfalls, which were, however, of much lower magnitude than those at La Réunion. World-record values for durations from 1 min. to 2 yr. are listed. The envelope curve of these maxima may be defined by the expression R= 16.6 D0.475, where R is rainfall in inches and D is duration in hours.