The American paleontologist O. C. Marsh named "Sphenacodon" (from Greek ' "wedge" + ' "point" + "" (-"odon") "tooth") in 1878, based on part of a lower jaw (dentary) bone found in the redbeds of northern New Mexico by fossil collector David Baldwin. In his very short description of the jaw, Marsh cited the back teeth as characteristic ("crowns are much compressed, and have very sharp cutting edges without crenulations") and assessed the animal as "about six feet in length, and carnivorous in habit," although the rest of the skeleton was not known. He did not provide an illustration of the specimen. Marsh gave the genus the Latin specific name "ferox" "fierce" and erected the new family Sphenacodontidae, placed under the primitive reptilian order "Rhynchocephala" (=Rhynchocephalia), then including nearly all groups of early reptiles in addition to the living tuatara.