Abstract Aim To reconstruct the biogeographical history of New World emballonurid bats (tribe Diclidurini). Although bats are the second most species-rich order of mammals, they have not contributed substantially to our understanding of the historical biogeography of mammals in the Neotropics because of a poor fossil record. In addition, being the only group of mammals that fly, bats typically have large distributions with relatively few species endemic to restricted areas that are amenable to vicariant biogeographical approaches. Location Central and South America. Methods Phylogenetic analysis for comparing trees (PACT) is a new algorithm that incorporates all spatial information from taxon area cladograms into a general area cladogram. There were nine biogeographical areas identified in Central and South America for New World emballonurid bats. Molecular dating was used to incorporate the temporal aspect of historical biogeography. This method was compared with dispersal–vicariance analysis (DIVA), which assumes vicariance as the default mode of speciation. Results Of the 45 speciation events in a fully resolved phylogeny, eight that were hypothesized by DIVA as vicariance were considered by PACT as two peripheral isolations and six within-area events. DIVA was less parsimonious because it required six more post-speciation dispersal events in addition to the 73 hypothesized by PACT. DIVA reconstructed a widely distributed ancestor, suggesting that most dispersal events occurred earlier, whereas the ancestral area for PACT based on character optimization was the Northern Amazon, suggesting that dispersal events were more recent phenomena. Main conclusions The general area cladogram from PACT indicated that within-area events, and not vicariance, provide the major mode of speciation for New World emballonurid bats. There was no biological evidence supporting or rejecting sympatric speciation in New World emballonurid bats. However, the geological history, combined with fluctuations in temperature and sea level, suggested within-area speciation in a changing and heterogeneous environment in the Northern Amazon during the Miocene. This scenario is similar to the taxon-pulse hypothesis of biotic diversification, which posits repeated episodes of range expansions and contractions from a stable core area such as the Guiana Shield within the Northern Amazon.