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 Ptychodiscaceae Lemmerm. (1899)
Subfamily †Dinogymnioideae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
1 Genus †Dinogymnium Evitt, Clarke & Verdier (1967)
2 Genus †Alisogymnium Lentin & Vozzhennikova (1990)
3 Genus †Amphigymnium Lentin & Vozzhennikova (1990)
4 Genus †Yolkinigymnium Lentin & Vozzhennikova (1990)