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 Suessiales Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
see Order Dinococcales Pascher (1914)
Family Borghiellaceae Moestrup, K.C.R. Lindberg & Daugbjerg (2009)
see Family Phytodiniaceae G.A. Klebs (1912)
Genus Baldinia Gert Hansen & Daugbjerg (2007)