Published claims in 1887-1903 that the mole cricket Neocurtilla hexadactyla (Perty) occurs in Puerto Rico all seem to be derived from a misidentification made by Agustín Stahl, a medical practitioner and collector of natural history objects, published in 1882. That species does not seem now to occur in Puerto Rico and almost certainly never did. However, the opportunity still exists for it to colonize by wind-assisted flight from islands to the southeast just as we believe did the mole cricket Scapteriscus didactylus (Latreille) as an immigrant. Stahl evidently mistook the latter for the former. According to some subsequent authors, he also stated that it (the mole cricket now believed to be S. didactylus) arrived in the port of Mayagüez in a cargo of guano about 1850 from Peru and thus colonized Puerto Rico. We found no verification for that story, and we doubt it. The first detection of the presence of S. didactylus in Puerto Rico may have been by a French expedition in 1797, but this species may have been present much earlier. Two other species of Scapteriscus were later detected in Puerto Rico. One, S. abbreviatus Scudder, was detected in 1917 and likely arrived as a contaminant of ship ballast some time earlier, perhaps at the port of Mayagüez. The other, S. imitatus Nickle and Castner, was detected about 1940 and seems to have been introduced inadvertently, as a result of mistaken identity. In broad terms, S. didactylus, S. abbreviatus, and S. imitatus are adventive species (meaning they arrived from somewhere else and are not native) in Puerto Rico. The vernacular name changa in Puerto Rico is owned by S. didactylus, which is called West Indian mole cricket in the English-speaking Caribbean. Historical accounts suggest that populations of S. didactylus and of two pest Phyllophaga spp. (Coleoptera: Scarabaeidae) surged after 1876/1877 and declined after 1920. This coincidence suggests that the cause may have been the same. The cause of the rise might conceivably have been introduction of the mongoose Herpestes javanicus (E. Geoffroy St. Hilaire) in 1877 (because it may have destroyed vertebrate predators) and the cause of the decline might conceivably have been introduction of the toad Bufo marinus L. in 1920, because it is a predator of Phyllophaga and Scapteriscus.