Vertebrata Cuvier, 1812 - vertebrates see Infraphylum Vertebrata Lamarck, 1801
   Class Agnatha Cope, 1889 [paraphyletic]
     Subclass †Pteraspidomorphi Goodrich, 1909 see Class Pteraspidomorphi Goodrich, 1909
       Order †Heterostraci Lankester, 1868 - heterostracans see Subclass Heterostraci Lankester, 1868
         01 ?Family †Arandaspididae Ritchie & Gilbert-Tomlinson, 1977
         02 Family †Astraspidae Eastman, 1917 [monotypic] see Family Astraspididae Eastman, 1917, nom. praeval.
         03 Family †Eriptychiidae Tarlo, 1962 [monotypic]
         04 Family †Cyathaspididae Kiaer, 1932, nom. praeval.
         05 Family †Amphiaspidae see Family Amphiaspididae Obruchev, 1939
         06 Family †Corvaspidae Dineley, 1955 [monotypic] see Family Corvaspididae Dineley, 1955, nom. praeval.
         07 Family †Traquairaspididae Kiaer, 1932, nom. praeval.
         08 Family †Pteraspidae see Family Pteraspididae Claypole, 1885
         09 Family †Cardipeltidae Bryant, 1933
         10 Family †Drepanaspidae see Family Psammosteidae Traquair, 1896