Superphylum Deuterostomia Grobben, 1908 - deuterostomes see Infrakingdom Deuterostomia Grobben, 1908
   Phylum Chordata Bateson, 1885 - chordates
     Subphylum Craniata auct. see Subphylum Vertebrata Cuvier, 1812
       Vertebrata (Lamarck, 1801) - vertebrates see Subphylum Vertebrata Cuvier, 1812
         Myopterygii - myopterygians
           Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
             Grade Chondrichthiomorphi
               Class Chondrichthyes Huxley, 1880 - cartilaginous fishes
                 Subclass Holocephali Bonaparte, 1832
                   Superorder Holocephalimorpha (Lund, 1986)
                     Cochliodontomorpha
                       Order †Chondrenchelyiformes Moy-Thomas, 1939 [monotypic]
                         Family †Chondrenchelyidae Berg, 1940
                           1 Genus †Chondrenchelys Traquair, 1888
                           2 Genus †Harpagofututor Lund, 1982
                           3 Genus †Platyxystrodus Hay, 1899