After Turner & Burrow, 2011, with taxa from Carroll, 1988, Williams, G. S., 1999-2000

<==o †Xenacanthiformes Berg, 1940 [Xenacanthida Glikman, 1964]
   |?- †Wurdigneria Richter, 2005
   `==o †Diploselachidae Hampe, 2003 [non Dick, 1981?] [paraphyletic]
      |?- †Dicentrodus bicuspidatus Traquair, 1888
      |--+-- †Reginaselache morrisi Turner & Burrow, 2011; E.Carb. Aust.
      |  `--o †Diplodoselache Dick, 1981; Miss. Eu.
      |     |?- †?“D.antiqua
      |     |-- †D. woodi Dick, 1981
      |     `-- †D. parvulus
      `--+-- †Lebachacanthus
         `--+--o †Orthacanthus Agassiz, 1843 [Diplodus Agassiz, 1843; Didymodus Cope, 1883; Diacranodus Garman, 1885; Diplodus Woodward, 1889; Orthacanthus Fritsch, 1889; Xenacanthus Beyrich, 1946, Hotton, 1952, Berman, 1970] Carb.-Perm. Eu. Perm. NA. U. Dev or L. Carb. EAs.
            |  |-- †O. arcuatus (Newberry, 1856)
            |  |-- †O. cylindricus (Agassiz, 1843)
            |  |-- †O. compressus (Newberry, 1856) [=? Xenacanthus compressus]
            |  |-- †O. gibbosus
            |  |-- †O. senckenbergianus
            |  |-- †O. bohemicus
            |  |-- †O. texensis Johnson, 1999
            |  |-- †O. platypternus Johnson, 1999
            |  `-- †O. donnelljohnsi Johnson & Thayer, 2009
            `--+-- †Hagenoselache sippeli Hampe & Heidtke, 1997
               `--o †Xenacanthidae Fritsch, 1889b
                  |?- †Anodontacanthus acutus Davis, 1881b, U. Carb. Eu.
                  |?-o †Diacranodus [Didymodus, Dittodus] M.Dev.-L.Perm. NA.
                  |  |-- †D. platypternus (Cope, 1884)
                  |  |-- †D. texensis (Cope, 1884)
                  |  |-- †D. priscus Eastman, 1899
                  |  `-- †D. striatus Eastman, 1899
                  |?-o †Expleuracanthus
                  |  `-- †E. gaudryi
                  |?- †Iriodus [Expleuracanthus] L. Perm. Eu.
                  |?- †Phricacanthus biserialis Davis, 1874, Penn. Eu.
                  |?- †Platyacanthus ventricosus Fritsch, 1889b [Anodontacanthus] L. Perm. Eu.
                  |?- †Pleuracanthus decheni Penn. Eu.
                  |-- †Plicatodus jordani Hampe, 1995
                  `--+--o †Triodus Jordan, 1849 sensu Soler-Gijón & Hempe, 1998, and Hempe, 2003
                     |  |--o †Triodus Jordan, 1849
                     |  |  |-- †T. sesselis Jordan, 1849
                     |  |  |-- †T. kraetschmeri
                     |  |  `-- †T. elpia Johnson & Thayer, 2009
                     |  `--o †Bohemiacanthus Schneider, 1996 [Schneider & Zajíc, 1994] [Triodus Jordan, 1849 in partim]
                     |     |-- †B. carinatus [Triodus carinatus]
                     |     |-- †B. lauterensis [Triodus lauterensis]
                     |     |-- †B. palatinus [Triodus palatinus]
                     |     |-- †B. obscurus (Hampe, 1989) [Triodus obscurus Hampe, 1989 ]
                     |     `-- †B. serratus [Triodus serratus]
                     `--o †Xenacanthus [Hypospondylus, Orthacanthus] L. Perm. Eu. NA. 
                        |-- †X. compressus [=? Orthaganthus compressus (Newberry, 1856)]
                        |-- †X. decheni (Goldfuss, 1847)
                        |-- †X. gracilis (Newberry, 1875)
                        |-- †X. laevissimus (Agassiz, 1837)
                        |-- †X. meisenheimensis
                        |-- †X. moorei (Woodward, 1889) [Orthacanthus]
                        |-- †X. parvidens (Woodward, 1908)
                        |-- †X. sp. [Australia]
                        |-- †X. texanus
                        `-- †X. texensis [=? Orthacanthus texensis Johnson, 1999]

Reference(s):