Cosmopolitanism occurred recurrently during the geologic past, especially after mass extinctions, but the underlying mechanisms remain poorly known. Three theoretical models, not mutually exclusive, can lead to cosmopolitanism: (1) selective extinction in endemic taxa, (2) endemic taxa becoming cosmopolitan after the extinction and (3) an increase in the number of newly originated cosmopolitan taxa after extinction. We analyzed an updated occurrence dataset including 831 middle Permian to Middle Triassic ammonoid genera and used two network methods to distinguish major episodes of ammonoid cosmopolitanism during this time interval. Then, we tested the three proposed models in these case studies. Our results confirm that at least two remarkable cosmopolitanism events occurred after the Permian–Triassic and late Smithian (Early Triassic) extinctions, respectively. Partitioned analyses of survivors and newcomers revealed that the immediate cosmopolitanism event (Griesbachian) after the Permian–Triassic event can be attributed to endemic genera becoming cosmopolitan (model 2) and an increase in the number of newly originated cosmopolitan genera after the extinction (model 3). Late Smithian cosmopolitanism is caused by selective extinction in endemic taxa (model 1) and an increase in the number of newly originated cosmopolitan genera (model 3). We found that the survivors of the Permian–Triassic mass extinction did not show a wider geographic range, suggesting that this mass extinction is nonselective among the biogeographic ranges, while late Smithian survivors exhibit a wide geographic range, indicating selective survivorship among cosmopolitan genera. These successive cosmopolitanism events during severe extinctions are associated with marked environmental upheavals such as rapid climate changes and oceanic anoxic events, suggesting that environmental fluctuations play a significant role in cosmopolitanism.