Elotherium leidyanum was named by Marsh in Cope (1868) [Marsh 1893 refers Elotherium leidyanum to Ammodon (gen. nov.), says the species was "already described by the writer" with a reference of "Proc. Phila. Acad., vol. xxii, p. 3; and Geology of New Jersey, p. 740, 1868." The first reference is from 1870, and states that the new species Rhinoceros mutitanus was found "... in the same layer with the remains of Elotherium Leidyanum Marsh, ..." The second reference is an appendix to The Geology of New Jersey (1868) written by E. D. Cope (of all people) who attributes the name Elotherium leidyanum to Marsh, without any other reference. I'm not sure where this name would have been published before this.]. Its type specimen is YPM 12040, a tooth (right p4), and it is a 3D body fossil. Its type locality is Farmingdale, which is in a Hemingfordian terrestrial horizon in the Kirkwood Formation of New Jersey.

It was recombined as Ammodon leidyanus by Hay (1902), Troxell (1920); it was recombined as Daeodon leidyanum by Tedford and Hunter (1984), Lucas et al. (1997); it was recombined as Dinohyus leidyanus by Albright (1991); it was synonymized subjectively with Daeodon shoshonensis by Lucas et al. (1998); it was considered a nomen nudum by Rhoads (1903); it was misspelled as Ammodon leidyanus by Troxell (1920); it was recombined as Ammodon leidyanum by Marsh (1893), Albright (1999).