The middle Eocene ceratomorph Hyrachyus has been considered a pivotal genus in ceratomorph evolution, either as a transitional form from tapiroids to rhinocerotoids, giving rise to all later rhinocerotoids, or else as the sister taxon to other rhinocerotoids. Thus, Hyrachyus has been commonly chosen as an outgroup in phylogenetic analyses of rhinocerotoids. However, little has been published on the osteology of Hyrachyus, even though well-preserved craniodental and postcranial specimens of this taxon have been in collections for decades. Here, we describe and illustrate the cranial and postcranial osteology of Hyrachyus modestus, based mainly on the exceptionally preserved specimens housed at the American Museum of Natural History, specifically AMNH FM 12664. Our bone-by-bone description provides detailed information on the osteological morphology of Hyrachyus, which should be useful for phylogenetic analyses of both rhinocerotoids and perissodactyls in general, because it provides one of the more complete and best-preserved examples of the skeleton of an earlier Eocene perissodactyl.

The cranial morphology of Hyrachyus modestus shows a shallow narial notch, a lacrimal contacting the nasal, and a sphenorbital fissure closely situated to the anterior opening of the alisphenoid canal. In the basicranial region, there is a mastoid exposure of the petrosal between the occipital and the squamosal, and the posttympanic process and paracondylar process are partly fused. The postcranial morphology of Hyrachyus modestus includes the following features: The cervical region of the vertebral column is relatively short compared to the rest of the vertebral column. The lumbar vertebrae have concave-convex embracing prezygapophyses and postzygapophyses. The scapula has a distinct acromion process. The humerus has a greater tubercle that does not elevate above the head, and the deltoid tuberosity and deltopectoral crest are weak. The scaphoid and lunar facets of the radius are confluent. The olecranon of the ulna extends posteroproximally. The manus is functionally tetradactyl, with a complete fifth manual digit. The innominate bone has a long, narrow coxal tuberosity. The greater trochanter of the femur is elevated proximally above the head. The femur has a long, narrow, and symmetric trochlea. The patella has a moderately anteroposteriorly deep base. The intercondyloid eminences of the tibia are equal in height, and the extensor sulcus of the tibia is relatively deep. The fibula has a relatively slender shaft with expanded ends. The pes has three functional digits. The calcaneus does not contact the navicular, nor does the Mt III contact the cuboid.

Comparisons between the skeleton of Hyrachyus modestus and those of the early tapiroid Heptodon, the hyracodontid Triplopus, the paraceratheriid Juxia, and the rhinocerotid Uintaceras were also investigated. These results indicate that Hyrachyus probably did not derive from Heptodon, but from a more basal group of ceratomorphs. Furthermore, distinct differences between the skeletons of Hyrachyus and Triplopus (the earliest representative of Hyracodontidae) suggest that hyracodontids were not descended from Hyrachyus. However, Hyrachyus-like ancestors probably gave rise to other non-hyracodontid rhinocerotoids. Like that of other Eocene perissodactyls, the postcranial morphology of Hyrachyus modestus exhibits adaptations that suggest that cursorial locomotion was already present early in perissodactyl evolution.