We quantified long-term successional trajectories of canopy arthropods on six tree species in a tropical rainforest ecosystem in the Luquillo Mountains of Puerto Rico that experienced repeated hurricane-induced disturbances during the 19-yr study (1991–2009). We expected: 1) differential performances of arthropod species to result in taxon- or guild-specific responses; 2) differences in initial conditions to result in distinct successional responses to each hurricane; and 3) the legacy of hurricane-created gaps to persist despite subsequent disturbances. At least one significant effect of gap, time after hurricane, or their interaction occurred for 53 of 116 analyses of taxon abundance, 31 of 84 analyses of guild abundance, and 21 of 60 analyses of biodiversity (e.g., richness, evenness, dominance, and rarity). Significant responses were ~60% more common for time after hurricane than for gap creation, indicating that temporal changes in habitat during recovery were of primary importance. Both increases and decreases in abundance or diversity occurred in response to each factor. Guild-level responses were probably driven by changes in the abundance of resources on which they rely. For example, detritivores were most abundant soon after hurricanes when litter resources were elevated, whereas sap-suckers were most abundant in gaps where new foliage growth was the greatest. The legacy of canopy gaps created by Hurricane Hugo persisted for at least 19 yr, despite droughts and other hurricanes of various intensities that caused forest damage. This reinforces the need to consider historical legacies when seeking to understand responses to disturbance.