Superphylum Deuterostomia Grobben, 1908 - deuterostomes see Infrakingdom Deuterostomia Grobben, 1908
   Phylum Chordata Bateson, 1885 - chordates
     Subphylum Craniata auct.
       Vertebrata Lamarck, 1801 - vertebrates see Infraphylum Vertebrata Lamarck, 1801
         Superclass †Pteraspidomorphi Goodrich, 1909 [monotypic]
           Class †Pteraspidomorphi Goodrich, 1909 see Class Pteraspidomorpha
             Subclass †Heterostraci Lankester, 1868
               1 ?Genus †Aserotaspis Dineley & Loeffler, 1976
               2 ?Order †Cardipeltida see Order Cardipeltiformes Bryant, 1933
               3 ?Order †Corvaspidida see Order Corvaspidiformes Stensiö, 1964
               4 ?Order †Lepidaspidida see Order Lepidaspidiformes Halstead, 1993
               5 ?Order †Tesseraspidida see Order Tesseraspidiformes Halstead, 1962
               6 ?Order †Traquairaspidiformes Stensio, 1958
               7 ?Order †Tolypelepidida see Order Tolypelepidiformes
               8 Order †Cyathaspidiformes Kiaer, 1930
               9 Order †Pteraspidiformes Berg, 1940