Class Dinophyceae Pascher (1914)
   01 Order Actiniscales Sournia (1984)
   02 Order Brachidiniales A.R. Loebl. ex Sournia (1984)
   03 Order Dinophysiales Kof. (1926) see Order Dinophysales Er. Lindem. (1928)
   04 Order Gymnodiniales Apstein (1909)
   05 Order Noctilucales Haeckel (1894)
   06 ?Order Oxyrrhinales Sournia (1984) see Order Oxyrrhida Sournia, 1990
   07 Order Peridiniales Haeckel (1894)
   08 Order Prorocentrales Lemmerm. (1910)
   09 Order Pyrocystales Apstein (1909) see Order Gonyaulacales F.J.R. Taylor (1980)
   10 Order Suessiales Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) see Order Dinococcales Pascher (1914)
   11 Order Thoracosphaerales Tangen (1982) see Order Peridiniales Haeckel (1894)