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