Division Dinoflagellata Engl. (1903) see Superclass Dinoflagellata Bütschli, 1885
   Subdivision Dinokaryota Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) see Superclass Dinokaryota Fensome et al., 1993
     Class Dinophyceae Pascher (1914)
       Subclass Peridiniphycidae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
         Order Peridiniales Haeckel (1894)
           1 Suborder Glenodiniineae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) [monotypic] see Order Thoracosphaerales Tangen (1982)
           2 Suborder Heterocapsineae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) [monotypic] see Order Peridiniales Haeckel (1894)
           3 Suborder Peridiniineae Poche (1913) see Order Peridiniales Haeckel (1894)
           4 Genus Chalubinskia Wolosz. (1916), incertae sedis
           5 Genus Staszicella Wolosz. (1916), incertae sedis
           6 Genus Thaurilens Pavillard (1917), incertae sedis