After Arratia & Tischlinger, 2010

<==o †Crossognathiformes Taverne, 1989
   |?-o †Varasichthyidae [basal Teleostei sensu Arratia, 2013]
   |  |?- †Bobbichthys opercularis
   |  |-- †Domeykos profetaensis Arratia & Schultze, 1985; L.Jur. SA.
   |  `--+-- †Luisichthys vinalensis White, 1942; L.Jur. WInd.
   |     |-- †Varasichthys ariasi Arratia, 1981, L.Jur. SAm.
   |     `--o †Protoclupea L.Jur. SAm.
   |        |-- †P. atacamensis Arratia & Schultze, 1985
   |        |-- †P. chilensis Arratia, Chang & Chong
   |        `?- †P. sp.
   `--+-- †Chongichthys dentatus Arratia, 1982 [Chongichthyidae]
      `--+-- †Bavarichthys incognitus Arratia & Tischlinger, 2010
         `--+-- †Notelops brama (Agassiz, 1841) Woodward, 1901; L. Cret. SA. [Notelopidae Forey, 1977]
            `--+--o †Crossognathoidei
               |  `--o †Crossognathidae
               |     |--o †Apsopelix  [Helmintholepis; Leptichthys; Palaeoclupea; Pelecorapis; Syllaemus] L.Cret. Eu. NA. 
               |     |  |?- †A. agilis
               |     |  `-- †A. anglicus Teller-Marshall & Bardack, 1978
               |     `--o †Crossognathus L.Cret. Eu. 
               |        |-- †G. sp.
               |        `-- †G. sabaudianus Wenz, 1965
               `--o †Pachyrhizodontoidei Forey, 1977
                  `--o †Pachyrhizontidae Cope, 1872
                     |-- †Goulmimichthys arambourgi Cavin, 2001
                     |-- †Rhacolepis buccalis Agassiz, 1841; L.Cret. SA.
                     `?-o †Pachyrhizodus Dixon, 1850 sensu Forey, 1977 [Raphiosaurus Owen, 1840; Thrissopater GŁnther, 1872] L.Cret. Eu. NA. Aus. [untreated by Arratia & Tischlinger]
                        |-- †P. megalops (Woodward, 1901) [Thrissopater megalops Woodward, 1901]
                        |-- †P. salmoneus (GŁnther, 1872) [Thrissopater salmoneus GŁnther, 1872]
                        |-- †P. magnus (Woodward, 1908) [Thrissopater magnus Woodward, 1908]
                        |-- †P. subulidens (Owen, 1840) [Raphiosaurus subulidens owen, 1840]
                        |-- †P. basalis Dixon, 1850 [incl. Pachyrhizodus gardneri (Mason, 1869)]
                        |-- †P. dibleyi Woodward, 1901
                        `-- †P. marathonensis

Untreated †Pachyrhizontidae:

Aquilopiscis wilsoni Cumbaa & Murray 2008
    †Elopopsis Heckel, 1856; L.Cret. Eu. NAf. 
        †E. fenzli Heckel, 1856
        †E. microdon Heckel
        †E. heckeli Reuss
        †E. ziegleri (Marck)
        †E. crassus Dixon
    †Michin csernai Alvarado-Ortega et al. 2008
    †Nardopiscis cavini Taverne, 2008
    †Platinx macropterus (Taverne, 1980)

After Nelson, 1994 and Froese & Pauly, 2001 (based on Taverne, 1989??)

<==o †Crossognathiformes
   |--o †Crossognathoidei
   |  `--o †Crossognathidae
   |     |-- †Apsopelix [Helmintholepis; Leptichthys; Palaeoclupea; Pelecorapis; Syllaemus] U.Cret. Eu. NA. 
   |     `-- †Crossognathus L.Cret. Eu. 
   `--o †Pachyrhizodontoidei
      |--o †Notelopidae
      |  `-- †Notelops L.Cret. SA.
      `--o †Pachyrhizontidae
         |-- †Elopopsis U.Cret. Eu. NAf. 
         |-- †Pachyrhizodus [Raphiosaurus; Thrissopater] U.Cret. Eu. NA. Aus. 
         `-- †Rhacolepis L.Cret. SA. 

Reference(s):