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 Elasmobranchii Bonaparte, 1838 - shark-like fishes see Infraclass Elasmobranchii Bonaparte, 1838
                   Infraclass †Cladoselachimorpha see Superorder Cladoselachimorpha
                     ?Family †Falcatidae Zangerl, 1990, "nom. praeval."
                       1 Genus †Damocles Lund, 1986
                       2 Genus †Falcatus Lund, 1985