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?]
                   Family †Climatiidae Berg, 1940, "nom. praeval."
                     1 Genus †Brachyacanthus Egerton, 1860
                     2 Genus †Climatius Agassiz, 1845
                     3 Genus †Parexus Agassiz, 1845
                     4 Genus †Vernicomacanthus Miles, 1973