Superphylum Deuterostomia Grobben, 1908 - deuterostomes see Infrakingdom Deuterostomia Grobben, 1908
   Phylum Chordata Bateson, 1885 - chordates
     Subphylum Craniata auct.
       Vertebrata Lamarck, 1801 - vertebrates see Infraphylum Vertebrata Lamarck, 1801
         Myopterygii Janvier, 1978 - myopterygians
           Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
             Grade Chondrichthiomorphi see Grade Chondrichthyomorphi
               Class Chondrichthyes Huxley, 1880 - cartilaginous fishes
                 Subclass Holocephali Bonaparte, 1832
                   Superorder †Paraselachimorpha (Lund, 1977) see Subclass Holocephali Bonaparte, 1832
                     1.1 [plesion] Family †Gregoriidae Lund & Grogan, 2004
                     1.2.1 Order †Orodontiformes Zangerl, 1981 [monotypic]
                     1.2.2.1? Order †Petalodontiformes Zangerl, 1981
                     1.2.2.2 Order †Helodontiformes Patterson, 1965 [monotypic]
                     2.1 Order †Iniopterygiformes Zangerl & Case, 1973
                     2.2 Order †Debeeriiformes Grogan & Lund, 2000 [monotypic]
                     3? Order †Eugeneodontiformes Zangerl, 1981