Listed, without family-connection or in family not listed by Donoghue & Sweet, 2001:

AcodusA. kechikaensisAmorphognathusA. ordovicicus Branson & Mehl, 1933
        †A. tvaerensisA. superbusAnticostiodus Zhang & Barnes, 2000
        †A. fahraeusi Zhang & Barnes, 2000
        †A. boltoni Zhang & Barnes, 2000
    †Basselodus Aldridge, 1982
        †B. arcticus Aldridge, 1982
        †B. variabilis (Webers, 1966)
        †B. semisymmetricus (Hamar, 1966)
    †BelodinaB. confluens Sweet
    †Carniodus [is a rhipidognathid?]
    †CornuodusC. longibasis (Lindström)
    †CulumbodinaC. pennaC. occidentalisCurtognathus Branson & Mefl, 1933b
        †C. typa Branson & Mefl, 1933b
    †Dapsilodus Cooper, 1976
        †D. obliquicostatus (Branson & Mehl, 1933a)
    †DecoriconusD. fragilisDiaphorodusD. russoiDrepanodusD. arcuatus Pander
        †D. robustusErismodus Branson & Mehl, 1933a
        †E. typus Branson & Mehl, 1933a
        †E. radicans (Hinde, 1879)
    †ErraticodonE. balticusFahraeusodusF. marathonensisGamachignathusG. ensiferHamarodusH. europaeusHistiodella [is a rhipidognathid?]
        †H. sinuosaIstorinusI. erectus Kn¨pfer, 1967
    †JuanognathusJ. variabilis Serpagli
        †J. gananda? Cooper
        †J. jaanussoniJumudontusganandaKallidontusK. serratusK. nodosusLenodusL. variabilisMicrozarkodinaM. flabellum (Lindström)
        †M. parvaOepikodusO. communisOistodus Pander, 1856
        †O. lanceolatus (Pander, 1856)
        †“O.” venustus Stauffer, 1935a
        †“O.” pseudoabundans Schopf, 1966
    †Oulodus Branson & Mehl, 1933b
        †O. serratus (Stauffer, 1930) [taxonomic history]
        †O. expansus (Armstrong, 1990)
        †O. ulrichiO. rohneriO. jeannae Schönlaub, 1975
        †O. panuarensis Bischoff, 1986
    †ParoistodusP. originalisP. horridusP. h. primusP. h. secundusPedavisP. latialata (Walliser, 1964)
        †P. sp. aff. P. thorsteinssoni Uyeno, 1980
        †P. thorsteinssoni Uyeno, 1980
    †PhragmodusP. undatusPolonodusP.galerusP. magnumPseudobelodina Sweet, 1979b
        †P. kirki (Stone & Furnish, 1959)
        †P. vulgarisP. inclinataP. manitoulinensis Leslie, 2000
    †Pseudooneotodus Drygant, 1974a
        †P. beckmanni (Bischoff & Sannemann, 1958) [Oneotodus? beckmanni Bischoff & Sannemann, 1958]
        †P. mitratus (Moskalenko, 1973)
    †PteracontiodusP. cryptodensPterospathodusP. amorphognathoidesPygodusP. anitaeScabbardellaS. altipesScolopodusS. quadratus Pander
    †Scyphiodus Stauffer, 1935b
        †S. primus Stauffer, 1935b
    †SpinodusS. spinatusStaufferella Sweet, Thompson & Satterfield, 1975
        †S. falcata (Stauffer, 1935c)
        †S. polonica (Spassov & Teller, 1963)
    †Stereoconus Branson & Mehl, 1933a
        †S. gracilis Branson & Mehl, 1933a
        †S. plenus Branson & Mehl, 1933a
    †StrachanognathusS. parvusStreptognathusS. pawhuskaensis (Harris & Hollingsworth, 1933)
        †S. zethus Chernykh & Reshetkova, 1987
    †TaoqupognathusT. blandus An
    †TripodusT. laevisTropodusT. comptus (Branson & Mehl)
        †T. sweeti (Serpagli)
    †WalliserodusW. curvatus (Branson & Branson, 1947)
        †W. amplissimusYaoxianognathus An, 1985
        †Y. wrighti Savage
        †Y. yaoxianensis An, 1985
        †Y. abruptus (Branson & Mehl, 1933b)

    †Paracordylodontidae Bergström, 1981
        †Paracordylodus gracilis Lindström, 1955

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