Superphylum Deuterostomia Grobben, 1908 - deuterostomes see Infrakingdom Deuterostomia Grobben, 1908
   Phylum Chordata Bateson, 1885 - chordates
     Subphylum Craniata auct. see Subphylum Vertebrata Cuvier, 1812
       Vertebrata (Lamarck, 1801) - vertebrates see Subphylum Vertebrata Cuvier, 1812
         Myopterygii - myopterygians
           Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
             Grade Teleostomi Bonaparte, 1836
               Class †Acanthodii Owen, 1846
                 Order †Climatiiformes Berg, 1940 [paraphyletic?]
                   Family †Climatiidae Berg, 1940
                     1 Genus †Brachyacanthus Egerton, 1860
                     2 Genus †Climatius Agassiz, 1845
                     3 Genus †Parexus Agassiz, 1845
                     4 Genus †Vernicomacanthus Miles, 1973