Class Dinophyceae Pascher (1914)
   Order Peridiniales Haeckel (1894)
     001 Family Amphidomataceae Sournia (1984)
     002 Family Ceratiaceae Kof. (1907)
     003 Family Ceratocorythaceae Er. Lindem. (1928) see Family Protoceratiaceae Er. Lindem. (1928)
     004 Family Cladopyxidaceae F. Stein (1883)
     005 Family Crypthecodiniaceae Biecheler ex Chatton (1952)
     006 Family Goniodomataceae Er. Lindem. (1928) see Family Thoracosphaeraceae J. Schiller (1930)
     007 Family Gonyaulacaceae Er. Lindem. (1928)
     008 Family Heterocapsaceae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
     009 Family Heterodiniaceae Er. Lindem. (1928)
     010 Family Ostreopsidaceae Er. Lindem. (1928)
     011 Family Oxytoxaceae Er. Lindem. (1928)
     012 Family Peridiniaceae Ehrenb. (1831)
     013 Family Protoperidiniaceae Balech (1988), nom. cons.
     014 Family Podolampadaceae Er. Lindem. (1928)
     015 Family Pyrophacaceae Er. Lindem. (1928) see Family Pyrocystaceae (F. Schütt) Lemmerm. (1899)
     080 Genus Amphidiniella T. Horig. (1995), incertae sedis
     108 Genus Adenoides Balech (1956), incertae sedis
     109 Genus Herdmania J.D. Dodge (1981), incertae sedis
     110 Genus Spiraublax Kofoid (1911), incertae sedis see Genus Spiraulax Kof. (1911)