Class †Placodermi McCoy, 1848
   Order †Arthrodira Woodward, 1891 see Order Arthrodiriformes Grande & Eastman, 1986
     Suborder †Brachythoraci Gross, 1932
       .1 Genus †Dunkleosteus Lehman, 1956
       .2 Genus †Coccosteus Miller, 1841
       .3 Genus †Tafilalichthys Lehman, 1956
       .4 Genus †Melanosteus Lelièvre & Goujet, 1987
       .5 Genus †Gymnotrachelus Dunkle & Bungart, 1939
       .6 Genus †Heintzichthys Whitley, 1933
       .7 Genus †Holonema Newberry, 1890
       .8 Genus †Goodradigbeeon White, 1978
       .9 Genus †Livosteus Obrucheva, 1962
       1 Genus †Maideria H. Lelièvre, 1995, incertae sedis
       2 Genus †Buchanosteus Stensiö, 1945, incertae sedis
       3 †"Migmatocephala" see Suborder Brachythoraci Gross, 1932
       3.1 Genus †Taemasosteus White, 1952
       3.2.1 Genus †Tityosteus Gross, 1960
       3.2.2.1 Genus †Antineosteus H. Lelièvre, 1984
       3.2.2.2 Family †Homostiidae Jaekel
       4 †"Eubrachythoraci" Miles, 1971