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 Suessiaceae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
             1 Genus †Suessia Morbey (1975)
             2 Genus †Beaumontella Below (1987)
             3 Genus Biecheleria Moestrup, K.C.R. Lindberg & Daugbjerg (2009)
             4 Genus Biecheleriopsis Moestrup, K.C.R. Lindberg & Daugbjerg (2009)
             5 Genus †Noricysta Bujak & Fisher (1976)
             6 Genus Pelagodinium Siano, Montresor, Probert & de Vargas (2010)
             7 Genus Polarella Montresor, Procaccini & Stoecker (1999)
             8 Genus Protodinium Lohmann (1908)
             9 Genus †Wanneria Below (1987)