Subphylum [Vertebrata] Cuvier, 1812 - vertebrates see Infraphylum Vertebrata Lamarck, 1801
   Class Agnatha Cope, 1889
     Subclass †Thelodonti Kiaer, 1932
       Order †Furcacaudiformes Wilson & Caldwell, 1998 - fork-tailed thelodonts
         ?Family †Barlowodidae Märss, Wilson & Thorsteinsson, 2002
           Genus †Barlowodusᵀ Märss, Wilson & Thorsteinsson, 2002
             †Barlowodus excelsusᵀ Märss, Wilson & Thorsteinsson, 2002