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]
?Genus Ceratoperidinium Margalef ex A.R. Loebl. (1980) [monotypic]