Acheloma was named by Edward Drinker Cope in 1882 based on a partial skull with associated postcranial elements from the Arroyo Formation of Texas;[3] the specimen is currently reposited at the American Museum of Natural History in New York.

Subsequent discoveries of large trematopids from the Arroyo Formation were named as different species of Trematops (T. milleri, T. willistoni), but these have since been synonymized with Acheloma cumminsi.

A second species of Acheloma was described by Polley & Reisz (2011) from the Richards Spur locality in Oklahoma.

[4] Schoch & Milner (2014) provide nine characters in their diagnosis of Acheloma: (1) toothed crest on the vomer extending medial to the internal naris; (2) constricted otic notch with nearly horizontal ventral margin; (3) preorbital region twice as long as the skull table; (4) naris twice as long as the orbit; (5) posterior skull table wide and posterolaterally expanded; (6) skull margin widens at level of and posterior to orbit; (7) palatine and ectopterygoid with tall fangs; (8) large intervomerine fenestra; and (9) choana elongate and curved with a Y-shaped contour.

[4] Sclerocephalus haeuseri Micromelerpeton credneri Micropholis stowi Eoscopus lockardi Cacops morrisi Phonerpeton pricei Acheloma cumminsi Acheloma dunni Actiobates peabodyi Ecolsonia cutlerensis Anconastes vesperus Tambachia trogallas