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)
             Family Congruentidiaceae J. Schiller (1935), nom. rej. see Family Protoperidiniaceae Balech (1988), nom. cons.
               1 Subfamily Congruentidioideae J. Schiller (1935) see Subfamily Protoperidinioideae
               2 Subfamily Diplopsalioideae Abé (1981) see Family Diplopsaliaceae Matsuoka (1988)