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Abstract Aim R. J. Whittaker et al. recently proposed a ‘general dynamic model of oceanic island biogeography’ (GDM), providing a general explanation of island biodiversity patterns by relating fundamental biogeographical processes – speciation, immigration, extinction – to area (A) and time (T; maximum island geological age). We adapt their model, which predicts a positive relationship with area combined with a humped relationship to time (designated the ATT2 model), to study the factors promoting diversification on the Azores for several arthropod groups. Location The Azorean archipelago (North Atlantic; 37–40° N, 25–31° W). Methods We use the number of single-island endemics (SIEs) as a measure of diversification, to evaluate four different predictions for the variation in SIEs between different islands, derived from the GDM theory and our knowledge of the fauna and history of the Azores. We calculated the number of SIEs for seven out of the nine Azorean islands and six groups of species (all arthropods, beetles, cavernicolous and non-cavernicolous species, and taxa with high and low dispersal abilities). Several variables accounting for island characteristics (area, geological age, habitat diversity and isolation) and generalized linear models were used to evaluate the reliability of each prediction. Results A linear and positive relationship between SIEs and an AT (area + time) model was the most parsimonious explanation for overall arthropod diversification. However, cavernicolous species showed the opposite pattern (more SIEs inhabiting the youngest islands). Also, isolation was an important predictor of diversification for all groups except for the species with high dispersal ability; while the former were negatively related to the distance from the main source of colonizing lineages (Santa Maria island in most cases), the latter were related to area. Dispersal ability was also a key factor affecting the diversification of most groups of species. Main conclusions In general, the diversification of Azorean arthropods is affected by age, area and isolation. However, different groups are affected by these factors in different ways, showing radically different patterns. Although the ATT2 model fails to predict the diversification pattern of several groups, it provides a framework for integrating these deviations into a general theory. Further improvements of the GDM theory need to take into account the particular traits of each group and the role of isolation in shaping island diversity.