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 Circospyridinae Haeckel, 1881
             1 Genus Amphispyris Haeckel, 1881
             2 Genus Archicircus Haeckel, 1887
             3 Genus Circospyris Haeckel, 1881
             4 Genus Lithocircus Müller, 1856
             5 Genus Sphaerospyris Haeckel, 1887
             6 Genus Spyridobotrys Haeckel, 1862
             7 Genus Toxarium Haeckel, 1887
             8 Genus Toxidium Haeckel, 1887, nom. illeg. see Genus Toxidiella Loeblich & Tappan, 1961