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 Pfiesteriaceae Steid. & J.M. Burkh. (1996) see Family Oodiniaceae Chatton (1920)
               Genus Stoeckeria H.J. Jeong, Jae S. Kim, J.Y. Park, Jong H. Kim, Sang Kim, I. Lee, Seung H. Lee, J.H. Ha & W.H. Yih (2005), incertae sedis