Halecostomi Regan, 1923
   Order †Pycnodontiformes Berg, 1937
     1 Family †Palaeobalistidae Blot, 1987, incertae sedis [monotypic] see Subfamily Nursalliinae Blot, 1987
     2 Family †Nursalliidae Blot, 1987, incertae sedis [monotypic] see Subfamily Nursalliinae Blot, 1987
     3 Family †Hadrodontidae Thurmond & Jones, 1981, incertae sedis [monotypic]
     4 Family †Trewavasiidae incertae sedis
     5 Family †Coccodontidae Berg, 1940, incertae sedis [monotypic]
     6 Family †Gibbodontidae [monotypic]
     7.1 Suborder †Gyrodontoidei Nursall, 1996
     7.2 Suborder †Pycnodontoidei Nursall, 1996