The oldest neoselachian elasmobranchs belong to the family Anachronistidae and possess a unique tooth morphology. Here, we review and redescribe all known anachronistid taxa, erect two new genera (Gunnellia and Turovella) and establish a new order to embrace the group–the Anachronistiformes. The anachronistids appeared in the Late Viséan (Mississippian, Carboniferous), radiated quickly, and disappeared by the end of the Guadalupian (Permian). Three anachronistid genera appeared in the early Carboniferous of modern Europe, but during the Pennsylvanian and Permian the various species of Cooleyella became widespread outside the area of anachronistid origins, even reaching Gondwana. Gunnellia:urn:lsid:zoobank.org:act:956FDF57-729C-42A4-B630-6C77C5FC6E87 Gunnellia:tatianae:urn:lsid:zoobank.org:act:1257710C-F466-4F21-9405-B43A8E0ED293 Turovella:urn:lsid:zoobank.org:act:FF92E89C-2FA9-4813-9B12-97A8B2056C72 Turovella:lebedevi:urn:lsid:zoobank.org:act:EC036A4A-BA2B-4E50-B302-33EF22C9E856.