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 Ptychodiscoideae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) [monotypic]
1 Genus Ptychodiscus F. Stein (1883)
2 Genus Balechina Loebl. & A.R. Loebl. (1968)
3 Genus Berghiella Kof. & J.R. Michener (1911)
4 ?Genus Ceratoperidinium Margalef ex A.R. Loebl. (1980) [monotypic]
5 ?Genus Lissaiella Lindemann (1928)
see Genus Amphidinium Clap. & J. Lachm. (1859)
6 ?Genus Lophodinium Lemmerm. (1910)