Phylum Radiolaria Müller, 1858 see Subphylum Radiozoa Cavalier-Smith, 1987
   Superclass Polycystina Ehrenberg, 1838 see Superclass Polycystinia Ehrenberg, 1838
     Class Nassellaria Ehrenberg, 1847
       Order Spyridinata Ehrenberg, 1847
         Family Acanthodesmiidae Haeckel, 1862
           Subfamily †Perispyridinae Haeckel, 1881
             1 Genus †Lithotympanum Haeckel, 1881
             2 Genus †Microcubus Haeckel, 1881
             3 Genus †Perispyris Haeckel, 1881
             4 Genus †Tricolospyris Haeckel, 1881