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 Teleostomi Bonaparte, 1836 see Clade Pan-Osteichthyes Rowe 2004 [Moore & Near 2020]
               Euteleostomi - bony vertebrates see Clade Osteichthyes Huxley 1880 [Moore & Near 2020]
                 Class Actinopterygii Woodward, 1891 - ray-finned fishes see Clade Actinopterygii Woodward 1891 [Moore & Near 2020]
                   Subclass Neopterygii Regan, 1923
                     Order †Aspidorhynchiformes Bleeker, 1859 [monotypic]
                       Family †Aspidorhynchidae Bleeker, 1859
                         1 Genus †Aspidorhynchus Agassiz, 1833
                         2 Genus †Belonostomus Agassiz, 1834
                         3 Genus †Vinctifer Jordan, 1920