The genus Peripristis was established in 1870 by Orestes H. St. John for the reception of two species of Carboniferous fish-remains, one of which had been previously described by Newberry & Worthen under the name of Ctenoptychius semicircularis, and was selected as type of the new genus. The other was known in collections and printed catalogues under Agassiz's manuscript title of Pristodus falcatus, but this name did not acquire validity until J. W. Davis adopted it in his monograph of 1883. As there can be no question that the two species are congeneric, it follows that St. John's appellation of Peripristis has priority over Davis' term, and the type species becomes P. semicircularis (N. & W.) instead of P. falcatus, Davis.