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]
               Class †Acanthodii Owen, 1846 - acanthodians
                 Order †Climatiiformes Berg, 1940 [paraphyletic?]
                   1 Genus †Nostolepis Pander, 1856, incertae sedis
                   2 Family †Climatiidae Berg, 1940, "nom. praeval."
                   3 Family †Culmacanthidae Long, 1983
                   4 Family †Diplacanthidae Bleeker, 1859
                   5 Family †Gyracanthidae Woodward, 1906
                   6 Family †Euthacanthidae Berg, 1940