Superphylum Deuterostomia Grobben, 1908 - deuterostomes see Infrakingdom Deuterostomia Grobben, 1908
   Phylum Chordata Bateson, 1885 - chordates
     Subphylum Craniata auct.
       Infraphylum Vertebrata Lamarck, 1801 - vertebrates
         Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
           Eugnathostomata
             Grade Teleostomi Bonaparte, 1836 see Clade Pan-Osteichthyes Rowe 2004 [Moore & Near 2020]
               Class †Acanthodii Owen, 1846 [paraphyletic?] - acanthodians
                 Order †Climatiiformes Berg, 1940 [paraphyletic]
                   1 Genus †Paucicanthus Hanke, 2002, incertae sedis
                   2 Genus †Ptomacanthus Miles, 1973, incertae sedis
                   3 Genus †Nostolepis Pander, 1856, incertae sedis
                   4 Family †Brochoadmonidae Bernacsek & Dineley, 1977
                   5 Family †Climatiidae Berg, 1940, "nom. praeval."
                   6 Family †Gyracanthidae Woodward, 1906
                   7 Family †Euthacanthidae Berg, 1940