Aim Data on Australian landbridge islands were analysed to seek relationships between the extinction of mammals on islands and a number of variables related to the islands, the native mammal species that occur on them and the presence or absence of exotic mammalian predators. The data base included attributes of the mammals (mean adult body weight, diet and shelter habitat) and of the islands [area, rainfall, presence/absence of significant areas of rockpile habitat, presence/absence of European red fox Vulpes vulpes Linnaeus, 1758, feral cat Felis catus Linnaeus, 1758, and rats Rattus rattus (Linnaeus, 1758) and R. exulans (Peale, 1848)]. Methods Statistical analysis of the 388 cases where a Critical Weight Range (CWR) mammal is extant and the forty-one cases where a CWR mammal is extinct was conducted using logistic regression to model the probability of extinction as a function of the island and mammal variables. Results Foxes and cats are correlated with CWR mammal extinctions, but cats are associated with extinctions particularly on more arid islands. Extinctions are more likely on islands with an absence of significant areas of rockpile habitat and where the native mammal is restricted to the ground's surface, and is relatively large. Conclusions An association between the presence of cats and native mammal extinctions has not previously been demonstrated for Australian islands. The introduction of exotic predators to Australian islands with native mammal species should be avoided and should any of these predators establish all means should be employed to eradicate them. For Australian continental islands the introduction of exotic predators, not habitat clearance, has been the major factor in extinctions.