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In 1933 George G. Simpson described a remarkably complete skull of Trigonostylops, an Eocene South American native ungulate (SANU) whose relationships were, in his mind, quite uncertain. Although some authorities, such as Florentino Ameghino and William B. Scott, thought that a case could be made for regarding Trigonostylops as an astrapothere, Simpson took a different position, emphasizing what would now be regarded as autapomorphies. He pointed out a number of features of the skull of Trigonostylops that he thought were not represented in other major clades of SANUs, and regarded these as evidence of its phyletic uniqueness. Arguing that the lineage that Trigonostylops represented must have departed at an early point from lineages that gave rise to other SANU orders, Simpson reserved the possibility that Astrapotheriidae might still qualify (in modern terms) as its sister group. Even so, he argued that the next logical step was to place Trigonostylops and its few known allies in a separate order, Trigonostylopoidea, coordinate with Astrapotheria, Notoungulata, Litopterna, and Pyrotheria. Simpson's classification was not favored by most later authors, and in recent decades trigonostylopids have been almost universally assigned to Astrapotheria. However, his evaluation of the allegedly unique characters of Trigonostylops and its allies has never been systematically treated, which is the objective of this paper. Using computed tomography, the skull of Trigonostylops is compared, structure by structure, to a variety of representative SANUs as well as extant perissodactylans (which together comprise the clade Panperissodactyla) and the "condylarthran" Meniscotherium. In addition to placing Simpson's character evaluations in a comparative context, we also provide detailed assessments of many vascular and pneumatization-related features of panperissodactylans never previously explored. Overall, we found that this new assessment strengthened the placement of Trigonostylops within a monophyletic group that includes Astrapotherium and Astraponotus, to the exclusion of other SANU clades. Although Trigonostylops cannot be considered as morphologically distinct or unusual as Simpson thought, our comparative and phylogenetic analyses have helped to generate a number of hypotheses about character evolution and function in SANUs that may now be fruitfully tested using other taxon combinations. Reconstruction of Trigonostylops wortmani by Jorge Blanco. [ABSTRACT FROM AUTHOR]