Superphylum Deuterostomia Grobben, 1908 - deuterostomes see Infrakingdom Deuterostomia Grobben, 1908
   Phylum Chordata Bateson, 1885 - chordates
     Subphylum Craniata auct.
       Infraphylum Vertebrata Lamarck, 1801 - vertebrates
         Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
           Eugnathostomata
             Grade Chondrichthyomorphi [monotypic]
               Class Chondrichthyes Huxley, 1880 - cartilaginous fishes
                 01 [stem] Genus †Obtusacanthus Hanke & Wilson, 2004
                 02 [stem] Family †Protodontidae Woodward, 1932
                 03 [stem] Family †Kathemacanthidae Gagnier & Wilson, 1996
                 04 [stem] Order †Polymerolepidiformes
                 05 [stem] Order †Omalodontiformes Turner, 1997
                 06 [stem] Order †Antarctilamniformes Ginter et al., 2008
                 07 ?Order †Mongolepidida Karatajute-Talimaa et al., 1990 see Order Mongolepidiformes
                 08 ?Family †Kannathalepididae Märss & Gagnier, 2001
                 09 ?Family †Wellingtonellidae Märss, Wilson & Thorsteinsson, 2002
                 10 ?Genus †Emsolepis Turner, 2004
                 11 [stem] Genus †Pucapampella Janvier & Suarez-Riglos, 1986
                 12 [stem] Genus †Plesioselachus Anderson, Long, Gess & Hiller, 1999
                 13 [stem] Genus †Gogoselachus Long et al., 2015
                 14 [stem] Family †Bandringidae Zangerl, 1969
                 15 [stem] Order †Phoebodontiformes Ginter, Hairapetian & Klug, 2002
                 16 Superorder †Cladoselachimorpha
                 17 Superorder †Ctenacanthimorpha
                 18 Superorder †Xenacanthimorpha
                 19.1 Subclass Holocephali Bonaparte, 1832
                 19.2 Subclass Euselachii Hay, 1902 - sharks, rays, and related fossils