[Phylum] Chordata Bateson, 1885 - chordates
   Subphylum Craniata auct.
     Infraphylum Vertebrata Lamarck, 1801 - vertebrates
       Superclass †Osteostracomorphi
         Class †Osteostraci Lankester, 1868
           Order †Cephalaspidiformes Halstead Tarlo, 1967
             Suborder †Ateleaspidoidei
               Family †Ateleaspididae Traquair, 1899, nom. praeval.
                 1 Genus †Ateleaspisᵀ Traquair, 1899
                 2 Genus †Hemicyclaspis Lankester, 1870
                 3 Genus †Hirella Cossmann, 1920
                 4 Genus †Aceraspis Kiaer, 1911