Phylum Dinoflagellata Engl. (1903) see Superclass Dinoflagellata Bütschli, 1885
   Subphylum Dinokaryota Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
     Class Dinophyceae Pascher (1914)
       Subclass Gymnodiniphycidae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
         Order Ptychodiscales Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) [monotypic]
           Family Brachydiniaceae Sournia (1972) see Family Brachidiniaceae Sournia (1972)
             1 Genus Brachydinium F.J.R. Taylor (1963) see Genus Brachidinium F.J.R. Taylor (1963)
             2 Genus Asterodinium Sournia (1972)
             3 Genus Microceratium Sournia (1972)