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 Gonyaulacales F.J.R. Taylor (1980)
           Family Thecadiniaceae Balech (1956), incertae sedis [monotypic]
             1 Genus Thecadinium Kof. & Skogsb. (1928)
             2 Genus Plagiodinium M.A. Faust & Balech (1993)
             3 Genus Planodinium R.D. Saunders & J.D. Dodge (1984)
             4 Genus Pseudothecadinium Hoppenrath & M.S. Selina (2006)
             5 Genus Thecadiniopsis Croome, Hallegr. & P.A. Tyler (1987)