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)
           Suborder Peridiniineae Poche (1913) see Order Peridiniales Haeckel (1894)
             1 Family Congruentidiaceae J. Schiller (1935), nom. rej. see Family Protoperidiniaceae Balech (1988), nom. cons.
             2 Family Peridiniaceae Ehrenb. (1831)
             3 Family Podolampaceae Er. Lindem. (1928) see Family Podolampadaceae Er. Lindem. (1928)
             4 Genus Amphidiniopsis Wolosz. (1929), incertae sedis
             5 Genus †Bellatudinium Yu et al. (1981), incertae sedis
             6 Genus †Octodinium Wrenn & Hart (1988), incertae sedis
             7 Genus †Umbodinium Bint (1983), incertae sedis