Class Dinophyceae Pascher (1914)
   Order Gymnodiniales Apstein (1909)
     1 Family Gymnodiniaceae Lank. (1885)
     2 Family Polykrikaceae Kof. & Swezy (1921) see Family Gymnodiniaceae Lank. (1885)
     3 Family Ptychodiscaceae Lemmerm. (1899)
     4 Family Warnowiaceae Er. Lindem. (1928)
     5 Genus Ceratoperidinium Margalef ex A.R. Loebl. (1980), incertae sedis