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 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 Peridiniaceae Ehrenb. (1831)
               01 Subfamily †Palaeoperidinioideae Bujak & Davies (1983)
               02 Subfamily †Deflandreoideae Bujak & Davies (1983)
               03 Subfamily Calciodinelloideae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) see Family Calciodinellaceae Deflandre (1947)
               04 Subfamily †Ovoidinioideae Bujak & Davies (1983)
               05 Subfamily †Wetzelielloideae Bujak & Davies (1983)
               06 Subfamily †Lithoperidinioideae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
               07 Subfamily Peridinioideae Bergh (1881)
               08 Genus †Maduradinium Cookson & Eisenack (1970), incertae sedis
               09 Genus †Morkallacysta Harris (1974), incertae sedis
               10 Genus †Muiradinium Harland & Sarjeant (1970), incertae sedis
               11 Genus Pentapharsodinium Indel. & A.R. Loebl. (1986), incertae sedis
               12 Genus †Talimudinium Mao & Norris (1988), incertae sedis
               13 Genus †Zhongyuandinium Zhu, He & Jin (1989), incertae sedis