The name-combination, _Pelodiscus agassizi_, was not generally accepted. Hay (1892:144) and Siebenrock (1924:188) referred _agassizi_ to the genus _Trionyx_. Hay regarded _agassizi_ as a full species (see discussion by Stejneger, 1944:73), whereas Siebenrock considered it a subspecies of _spiniferus_; both authors regarded _asper_ as a synonym of _agassizi_. Neither _asper_ nor _agassizi_ was mentioned in the first three editions of the Check List of North American Amphibians and Reptiles (Stejneger and Barbour, 1917, 1923, 1933); the same authors in the fourth (1939:171, 172) and fifth editions (1943:212, 213) listed _agassizi_ as a full species, and _asper_ as a subspecies of _spinifera_. Stejneger (1944) used the same arrangement as set forth in the fourth and fifth editions of the Check List, and distinguished _agassizi_ on the basis of cranial characters, namely, the small size of the internal choanae, the greater width of the alveolar surface of the lower jaw, and the position of the suture between the palatine and basisphenoid relative to the posterior edge of the temporal fossa. Neill (1951:9) regarded the peculiarities of the _agassizi_-type skull as inconstant, but recognized _agassizi_ (and _asper_) as a subspecies of _ferox_. Crenshaw and Hopkins (1955) showed that _asper_ did not intergrade with _ferox_. Schwartz showed that _agassizi_ did not intergrade with _ferox_, and regarded _agassizi_ as a synonym of _T. s. asper_ (1956:17), but stated that _agassizi_ possessed "wider crushing surfaces on the maxillae than does _T. s. asper_, even when skulls of the same size and sex are compared" (_op. cit._:9). The holotype of _Platypeltis agassizi_ (MCZ 37172) is a dried adult female consisting of shell, skull and limb bones; the carapace is approximately 300 millimeters long (Schwartz, _loc. cit._). I have examined only the skull of MCZ 37172 (Plate 54), and it is the largest of 12 _agassizi_-type skulls I have seen. The basicranial length is 72.5 millimeters, and the greatest width, which occurs at the level of the quadratojugals, is 52.9 millimeters. The _agassizi_-type skulls have been discussed under the subsection on variation. The type locality of _T. s. asper_, Lake Concordia, Louisiana (lower Mississippi River drainage) as restricted by Baur (1893:220), is in an area of intergradation of three subspecies of _Trionyx spinifer_ where most individuals are not typical of _asper_. The syntypes, the designation of MCZ 1597 as a lectotype, and Pearl River, Columbus, Marion County, Mississippi, as the type locality have been discussed elsewhere (Webb, 1960). The range of _T. s. asper_ overlaps that of _T. ferox_ in Georgia and South Carolina. The two species remain distinct in the area of overlap of their geographic ranges (Crenshaw and Hopkins, 1955:16; Schwartz, _op. cit._:5). _Trionyx s. asper_ intergrades with _T. s. hartwegi_ and _T. s. spinifer_ in the lower Mississippi Valley (Conant and Goin, 1948:11).