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
           1 Subfamily Circospyridinae Haeckel, 1881
           2 Subfamily †Perispyridinae Haeckel, 1881
           3 Subfamily Acanthodesmiinae Haeckel, 1862
           4 Subfamily Paradictyinae Haeckel, 1881 [monotypic]