Subphylum [Vertebrata] Cuvier, 1812 - vertebrates
   Class Agnatha Cope, 1889
     Subclass †Thelodonti Kiaer, 1932
       Order †Furcacaudiformes Wilson & Caldwell, 1998 - forktail thelodonts
         ?Family †Barlowodidae Märss, Wilson & Thorsteinsson, 2002
           Genus †Barlowodusᵀ Märss, Wilson & Thorsteinsson, 2002
             1 †Barlowodus excelsusᵀ Märss, Wilson & Thorsteinsson, 2002
             2 †Barlowodus floralis Märss, Wilson & Thorsteinsson, 2002
             3 †Barlowodus tridens Märss, Wilson & Thorsteinsson, 2002