[Phylum] Chordata Bateson, 1885 - chordates
   Subphylum Craniata auct.
     Infraphylum Vertebrata Lamarck, 1801 - vertebrates
       Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
         Class †Acanthodii Owen, 1846 - acanthodians
           Order †Climatiiformes Berg, 1940
             Family †Climatiidae Berg, 1940, "nom. praeval."
               1 Genus †Brachyacanthus Egerton, 1860
               2 Genus †Climatius Agassiz, 1845
               3 Genus †Parexus Agassiz, 1845