Contrary to morphological claims, molecular data indicate that the order Perissodactyla (e.g., horses, rhinoceroses, and tapirs) is neither part of the superordinal taxon Paenungulata (Sirenia, Proboscidea, and Hyracoidea) nor an immediate outgroup of the paenungulates. Rather, Perissodactyla is closer to Carnivora and Cetartiodactyla (Cetacea + Artiodactyla) than it is to the paenungulates. Therefore, two morphologically defined superordinal taxa, Altungulata (Proboscidea, Sirenia, Hyracoidea, and Perissodactyla) and Ungulata (Altungulata and Cetartiodactyla), are invalidated. Perissodactyla, Carnivora, and Cetartiodactyla are shown to constitute a rather tight trichotomy. However, a molecular analysis of 36 protein sequences with a total concatenated length of 7885 aligned amino acids indicates that Perissodactyla is closer to Cetartiodactyla than either taxa is to Carnivora. The relationships among Paenungulata, Primates, and the clade consisting of Perissodactyla, Carnivora, and Cetartiodactylaa could not be resolved on the basis of the available data. (C) 1997 Academic Press.