After Clement & Long, 2010, and Lloyd, Wang & Brusatte, 2012 (based on datasets from Schultze & Marshall, 1993, Schultze, 2001 and 2004); with untreated taxa from Carroll, 1988, Cloutier & Ahlberg, 1996

Note: Lloyd et al. don't give any supernominal names for nodes in their phylogenetic tree. Names which I have given to various nodes are those which has been previously used for Dipnoi. This is one of the aspects that clearly speak for comprehensive phylogeny-based taxonomic treatment for Dipnoi.

<==o Dipnoiformes Cloutier, 1990 [Dipnoi Müller, 1845] (lungfishes; keuhkokalat)
   |-- †Powichthys thorsteinssoni [Powichthyidae] L. Dev. NNA.
   `--+-- †Youngolepis preacursor Chang & Yu, 1981
      `--o Dipnoi Müller, 1845 [Dipneusti]
         |-- †Diabolepis speratus (Chang & Yu, 1984) Schultze, 1993 [=Diabolichthyes, preoccupied] [Diabolepididae Schultze, 1993]
         `--+--o ?†Dipnorhynchidae Berg, 1940
            |  |-- †Westollrhynchus lehmanni (Westoll, 1949) Schultze, 2001 [Dipnorhynchus lehmanni Westoll, 1949; Speonesydrion lehmanni (Westoll, 1949) Campbell & Barwick, 1985]
            |  `--+--o †Ichnomylax Long, Campbell & Barwick, 1994
            |     |  |-- †I. kurnai Long, Campbell & Barwick, 1994
            |     |  `-- †I. karatajae Reisz, Krupina & Smith, 2004
            |     `==o †Dipnorhynchus Jaekel, 1927; L.Dev. Eu., M.Dev. Aust.
            |        |-- †D. suessmilchi (Etheridge) Hills, 1941, Thomson & Campbell 1971 [Ganorhynchus sussmilchi Etheridge] [type]
            |        `--+-- †“Chirodipterusonawwayensis Schultze, 1982
            |           `--+-- †D. cathlesae Campbell & Barwick, 1999
            |              `-- †D. kurikae Campbell & Barwick, 1985
            `--+-- †“Dipnorhynchuskiandrensis Campbell & Barwick 1982
               `--+-- †Uranolophus wyomingensis L. Dev. NA. [Uranolophina: Uranolophidae Miles, 1977]
                  `--+-- †Speonesydrion iani Campbell & Barwick, 1983
                     `--+-- †Jarvikia arctica Lehman, 1959
                        `--+--+--o ?†Dipteridae Owen, 1846
                           |  |  |-- †Barwickia downunda Long, 1992a
                           |  |  `--o †Dipterus Sedgwick & Murchison, 1828 [Catopterus, Eoctenodus, Paradipterus, Polyphractus] L.-U. Dev. Eu. M.-U. Dev. NA. U. Dev. NAs. Aus.
                           |  |     |?- †D. oervigi Gross, 1964
                           |  |     `-- †D. valenciennesi Sedgwick & Murchison, 1828 [incl. Palaeospondylus gunni Traquair [Palaeospondyliformes: Palaeospondylidae:], a larval form]
                           |  `--o ?†Chirodipteridae Campbell & Barwick, 1990
                           |     |--+-- †Dipterus cf. valenciennesi
                           |     |  `-- †Chiropterus rhenanus Mörs, 1991
                           |     `--+-- †Adololopas moyasmithi Campbell & Barwick, 1998
                           |        `--o †Chirodipterus Gross, 1933; U. Dev. Eu. Aus.
                           |           |-- †C. australis Miles, 1977
                           |           |?- †C. liangchengi Song & Chang, 1991
                           |           |?- †C. potteri Kemp, 2000
                           |           `-- †C. wildungensis (Gross, 1933) [non Säve-Söderbergh, 1952]
                           `--+-- †Pillararhynchus longi Campbell & Barwick, 1990 [Chirodipteridae: Pillararhynchinae Long, 1992]
                              `--+--+-- †Sorbitorhynchus deleaskitus Wang, Drapala, Barwick & Campbell, in Campbell & Barwick, 1990 [Chirodipteridae: Pillararhynchinae Long, 1992]
                                 |  `-- †Melanognathus canadensis Jarvik, 1967; L. Dev. NNA.
                                 `--+-- †Palaeodaphus insignis (Gervais) [Palaedaphus; ?Archaeonectes; ?Heliodus; ?Paleodahus]; U.Dev. Eu. NAm.
                                    `--+-- †Sunwapta grandiceps Thomson, 1967
                                       `--+-- †Gogodipterus paddyensis (Miles, 1977) Long, 1992b [Chirodipterus paddyensis Miles, 1977]
                                          `--+--o †Stomiahykidae Bernacsek, 1977
                                             |  |-- †Stomiahykus thlaodus Bernacsek, 1977; M.Dev. NA.
                                             |  `-- †Amadeodipterus kencampbelli Young & Schultze, 2005; M.Dev. CAust.
                                             `--+-- †Tarachomylax oepiki Barwick, Campbell & Mark-Kurik, 1997
                                                `--+-- †Iowadipterus halli Schultze, 1992
                                                   `--+--o †Rhinodipterus Gross, 1959; M.-U. Dev. Eu. [Rhinodipteridae Campbell & Barwick, 1990]
                                                      |  |-- †R. secans Gross, 1959
                                                      |  |-- †R. ulrichi Ørvig, 1961
                                                      |  |-- †R. stolbovi Krupina, 1995
                                                      |  `-- †R. kimberleyensis Clement, 2012
                                                      `--+--o †Phaneropleuridae Huxley, 1861
                                                         |  |-- †Oervigia nordica Lehman, 1959; U.Dev. Gr.
                                                         |  `-- †Phaneropleuron andersoni U. Dev. Eu. ?Gr.
                                                         `--+?- †Harajicadipterus youngi Clement, 2009; M.Dev CAust.
                                                            |--o ?†Holodipterida Moy-Thomas & Miles, 1971
                                                            |  |-- †Orlovichthys limnatis Lehman, 1959 [non? Krupina, 1980]; U. Dev. EEu.
                                                            |  `--+--+--+-- †Scaumenacia curta (Whiteaves 1881) Traquair, 1893 [Canadipterus Jaekel, 1927; Canadiptarus (lapsus calami)] U. Dev. NA. ?Eu. 
                                                            |     |  |  `-- †Pentlandia macroptera (Traquair, 1888)  [Dipterus macroptera Traquair, 1888] M. Dev. Eu.
                                                            |     |  `--+-- †Howidipterus donnae Long, 1992a
                                                            |     |     `-- †Delatitia breviceps (Woodward, 1906) Long & Campbell, 1985
                                                            |     `--+--o †Fleurantiidae Berg, 1940
                                                            |        |  `-- †Fleurantia denticulata Graham Smith & Westoll 1937; U.Dev. NA.
                                                            |        `--o ?†Holodontoidei Schultze, 1992
                                                            |           |--o †Rhynchodipteridae Moy-Thomas, 1939 [non? Berg, 1940]
                                                            |           |  |--o †Griphognathus Gross, 1959
                                                            |           |  |  |-- †G. minutidens Gross, 1959
                                                            |           |  |  |-- †G. sculpta Schultze, 1969(?)
                                                            |           |  |  `-- †G. whitei Miles, 1977
                                                            |           |  `--+-- †Rhynchodipterus elginensis Säve-Söderbergh, 1937
                                                            |           |     `--+-- †Jessenia concentrica Otto & Bardenheuer, 1996 [non Jessenia, a synonym of Oenocarpus (a Brazilian palmtree)]
                                                            |           |        `--o †Soederberghia Lehman, 1959; U. Dev. Gr. Aus. NA.
                                                            |           |           |-- †S. groenlandica Lehman, 1959
                                                            |           |           `-- †S. simpsoni Ahlberg, Johanson & Daeschler, 2001
                                                            |           `--o †Holodontidae Gorizdro-Kulczycka, 1950 sensu Clement & Long, 2010b [HolodipteridaMoy-Thomas & Miles, 1971: Holodontoidei Schultze, 1992]
                                                            |              |--+-- †Archaeonectes pertusus Meyer, 1858
                                                            |              |  `-- †Robinsondipterus longi (Campbell & Barwick, 1991) Long, 2010 [Holodipterus longi Campbell & Barwick, 1991; Holodipterus (Holodipterus) longi Pridmore, Campbell & Barwick, 1994; Holodipterus (Robinsondipterus) longi]
                                                            |              `--+--o †Holodipterus White & Moy-Thomas, 1940 [Archaeotylus; Holodus; Holodipterus (Holodipterus) White & Moy-Thomas; Pridmore, Campbell & Barwick, 1994] U.Dev. EEu. Aust. 
                                                            |                 |  |-- †H. kiprijanovae (Pander) [type, suppressed?]
                                                            |                 |  `-- †H. gogoensis Miles, 1977 [Holodipterus (Holodipterus) gogoensis Pridmore, Campbell & Barwick, 1994]
                                                            |                 `--+-- †Xeradipterus hatcheri Clement & Long, 2010b; U.Dev. Aust.
                                                            |                    `--+-- †“Holodipterus” (Holodipteroides) elderae Pridmore, Campbell & Barwick, 1994
                                                            |                       `-- †Asthenorhynchus meemannae (Pridmore, Campbell & Barwick, 1994) Long, 2010 [Holodipterus (Asthenorhynchus) meemannae Pridmore, Campbell & Barwick, 1994]
                                                            `--+--+-- †Adelargo schultzeiJohanson & Ritchie, 2000; U.Dev. Aust.
                                                               |  `--o †Andreyeichthys Krupina, 1987 [non? Krupina & Reisz, 1999] SWNAm.
                                                               |     |?- †A. sp.
                                                               |     `-- †A. epitomus Krupina, 1987
                                                               `--+-- †“Holodipterussanctacrucensis Gorizdro-Kulczycka, 1950
                                                                  `-- Post-Devonian dipnoans [Ceratodiformes sensu lato]

Untreated Dipnoi:

Cathlorhynchus trismodipterus Campbell, Barwick & Senden, 2009
    †Ganorhynchus Traquair, 1873; M.-U.Dev. Eu. NAm.
        †G. beecheri (Newberry)
        †G. rigauxi (Dutertr, 1931)
        †G. woodwardi Traquair, 1878
        †G. splendens Gross, 1937
    †Erikia jarviki Chang & Wang, 1995
    †Iranorhynchus seyedemamii Janvier & Martin, 1978
    †Osteoplax erosus M'Coy, 1848; Penn. WEu.
    †Pinnalongus saxoni Newman & den Blaauwen, 2007; M.Dev. WEu.
    †Sinodipterus beibei Qiao " Zhu, 2009; M.Dev. EAs.

    †Dipteridae Owen, 1846
        †Conchodus jerofejewi (Pander, 1858) McCoy, 1848 [Creatodus lateralis: Eichwald, 1846; Cheirodus jerofejewi Pander, 1858; Cheirodus lateralis Eichwald, 1860; Conchodus jerofejewi (Pander, 1858) Krupina, 2004] M.-U. Dev. Eu. U. Dev. NA.
        †Dipteroides Jaekel, 1926 (or 1935); U.Dev. Eu.

Alternative phylogeinies of Dipnoiformes:

After Clement & Long, 2010 (fig. 10b)

<==o Dipnoiformes
   |-- †Diabolepis
   |-- †Tarachomylax
   `--+-- †Jessenia
      |-- †Stomiahykus
      |--+-- †Uranolophus
      |  `--+-- †Dipnorhynchus
      |     `--+-- †Ichnomylax
      |        `-- †Speonesydrion
      `--+-- †Gogodipterus
         `--+--+-- †Melanognathus
            |  `--+--+-- †Griphognathus
            |     |  `-- †Robinsondipterus
            |     `--+-- †Holodipterus gogoensis
            |        `--+-- †Xeradipterus
            |           `--+-- †“Holodipterus” (Holodipteroides) elderae
            |              `-- †Asthenorhynchus
            `--+--+-- †Chirodipterus australis
               |  `-- †Sorbitorhynchus
               `--+-- †Dipterus
                  `--+-- †Adololopas
                     `--+-- †Pillararhynchus
                        `--+-- †Orlovichthys
                           `--+--+-- †Soederberghia
                              |  `-- †Conchopoma
                              `--+-- †Andreyevichthys
                                 `--+--+-- †Scaumenacia
                                    |  `--+-- †Fleurantia
                                    |     `--+-- †Barwickia
                                    |        `-- †Howidipterus
                                    `--+-- †Ctenodus
                                       |-- †Sagenodus
                                       `--+-- †Gnathorhiza
                                          `-- Neoceratodus

After Qiao & Zhu, 2009

<==+-- †Youngolepis
   `--o Dipnoi
      |-- †Diabolepis
      `--+--+-- †Westollrhynchus
         |  `--+-- †Ichnomylax
         |     `--+-- †Dipnorhynchus sussmilchi
         |        `-- †Speonesydrion
         `--+-- †Uranolophus
            `--+-- †Stomiahykus
               `--+--+-- †Iowadipterus
                  |  `-- †Jessenia
                  `--+-- †Tarachomylax
                     |-- †Melanognathus
                     |-- †Gogodipterus
                     `--+-- †Dipterus
                        `--+--+-- †Adololopas
                           |  `--+-- †“Chirodipterusliangchangi
                           |     `--+-- †“Chirodipterusaustralis
                           |        `--+-- †Sorbitorhynchus
                           |           `-- †Pillararhynchus
                           `--+-- †Sinodipterus
                              `--+--+-- †Rhinodipterus
                                 |  `-- †Chirodipterus wildungensis
                                 |--+-- †Holodipterus
                                 |  `--+-- †Soederberghia
                                 |     `-- †Griphognathus
                                 `--+-- †Adelargo
                                    |-- †Fleurantia
                                    |--+-- †Howidipterus
                                    |  `-- †Barwickia
                                    `--+-- †Scaumenacia
                                       `--+-- †Andreyevichthys
                                          `-- †Orlovichthys

Reference(s):

  • Qiao, T. & Zhu, M., 2009: A new tooth-plated lungfish from the Middle Devonian of Yunnan, China, and its phylogenetic relationships.
    –Acta Zoologica: Vol. 90, pp. 236-252 [doi: 10.1111/j.1463-6395.2008.00381.x]

After Clement, 2009 (Fig. 4b)

<==o Dipnoiformes
   |-- †Diabolepis
   |--+-- †Jessenia
   |  `--+-- †Uranolophus
   |     `--+-- †Stomiahykus
   |        |-- †Dipnorhynchus sussmilchi
   |        `--+-- †Speonesydrion
   |           `-- †Ichnomylax
   `--+--+-- †Tarachomylax
      |  `-- †Melanognathus
      `--+-- †Dipterus
         |--o “Chirodipterid clade”
         |  |-- †Adololopas
         |  `--+-- †Sorbitorhynchus
         |     |-- †Pillararhynchus
         |     `--+-- †Gogodipterus
         |        `-- †Chirodipterus australis
         `--+-- †Harajicadipterus
            |--o “Holodontid clade”
            |  |--+-- †Holodipterus gogoensis
            |  |  `-- †Holodipterus (Asthenorhynchus) meemannae
            |  `--+-- †Holodipterus (Robinsondipterus) longi
            |     `-- †Griphognathus whitei
            `--+-- †Orlovichthys
               `--+--+-- †Conchopoma
                  |  `-- †Soederberghia
                  `--+-- †Andreyevichthys
                     `--+--+-- †Scaumenacia
                        |  `--+-- †Fleurantia
                        |     `--+-- †Howidipterus
                        |        `-- †Barwickia
                        `--+-- †Sagenodus
                           |-- †Ctenodus
                           `--+-- †Gnathorhiza
                              `-- Neoceratodus

Reference(s):

  • Clement, A. M., 2009: A new genus of lungfish from the Givetian (Middle Devonian) of central Australia.
    –Acta Palaeontologica Polonica: Vol. 54, #4, pp. 615-626 [doi: 10.4202/app.2008.0057]

After Friedman, M., 2007 (Fig. 19., 20.)

<==o Dipnoiformes
   |-- †Powichthys
   `--+-- †Youngolepis
      `--+-- †Diabolepis
         `--+--+-- †Dipnorhynchus sussmilchi
            |  `-- †Dipnorhynchus kurikae
            `--+-- †Uranolophus
               |-- †Stomiahykus
               `--+?- †Melanognathus
                  `--+--+-- †“Chirodipterusaustralis
                     |  `-- Gogodipterus
                     `--+-- †Pillararhynchus
                        `--+-- †Sorbitorhynchus
                           `--+-- †Dipterus valenciennesi
                              `--+?- †“Chirodipterusliangchengi
                                 `--+-- †Orlovichthys
                                    `--+-- †“Chirodipteruswildungensis
                                       `--+-- †Holodipterus gogoensis
                                          `--+-- †“Griphognathuswhitei
                                             `--+-- †Griphognathus minutidens
                                                `-- †Soederberghia

Reference(s):

  • Friedman, M., 2007: The interrelationships of Devonian lungfishes (Sarcopterygii: Dipnoi) as inferred from neurocranial evidence and new data from the genus Soederberghia Lehman, 1959.
    –Zoological Journal of the Linnean Society: Vol. 151, #1, pp. 115-171 [doi: 10.1111/j.1096-3642.2007.00320.x]

After Schultze, 2001

<==o Dipnoiformes
   |-- †Psarolepis
   |-- †Diabolepis
   `--+--+-- †Uranolophus
      |  `-- †Melanognathus
      `--+-- †Westollrhynchus sp.
         `--+--+--+-- †D. kurikae
            |  |  `-- †D. kiandrensis
            |  `--+-- †“Speonesydrion” iani
            |     `-- †D. suessmilchi
            `--+-- †Stomiahykus
               `--+-- †Jessenia
                  `--+-- †Iowadipterus
                     `--+--+-- †Pillararhynchus
                        |  `-- †Sorbitorhynchus
                        `--+-- †Tarachomylax
                           `--+-- †Dipterus
                              `--+-- †Adololopas
                                 `--+-- †Rhinodipterus
                                    `--+--+-- †Gogodipterus
                                       |  `-- †Chirodipterus
                                       `--+--+-- †Holodipterus
                                          |  `-- †Adelargo
                                          `--+--+-- †Howidipterus
                                             |  `--+-- †Barwickia
                                             |     `--+-- †Fleurantia
                                             |        `--+-- †Griphognathus
                                             |           `--+-- †Rhynchodipterus
                                             |              `--+-- †Soederberghia
                                             |                 `-- †Jarvikia
                                             `--+-- †Scaumenacia
                                                `--+-- †Pentlandia
                                                   `--+-- †Oervigia
                                                      `--+-- †Andreyevichthys
                                                         `--+-- †Phaneropleuron
                                                            `-- †Orlovichthys

Reference(s):

  • Schultze, H.-P., 2001: Melanognathus, a primitive dipnoan from the Lower Devonian of the Canadian Arctic and the interrelationships of Devonian dipnoans.
    –Journal of Vertebrate Paleontology: Vol. 21, #4, pp. 781-794 [doi: 10.1671/0272-4634(2001)021[0781:MAPDFT]2.0.CO;2]

After Carroll, 1988, and Cloutier & Ahlberg, 1996

<==o Dipnoiformes
   |--o †Powichthyidae
   |  `-- †Powichthys
   `--+-- †Youngolepis
      `--o Dipnoi
         |-- †Diabolepis
         `--+--o †Uranolophina
            |  `--o †Uranolophidae
            |     `-- †Uranolophus
            `--o Dipnorhynchina
               |?-o †Holodontidae
               |  |-- †Adelargo
               |  `-- †Holodipterus
               |--o †Rhynchodipteridae
               |  `-- †Rhinodipterus
               |--o †Dipnorhynchidae
               |  |-- †Dipnorhynchus
               |  |-- †Ganorhynchus
               |  |-- †Griphognathus
               |  `-- †Holodipterus
               |--o †Sagenodontidae
               |  |?- †Proceratodus
               |  |-- †Megapleuron
               |  |-- †Sagenodus
               |  `-- †Straitonia
               `--o Speonesydrionina
                  |?- †Osteoplax
                  |?- †Palaeophichthys
                  |--o †Dipteridae
                  |  |?- †Palaedaphus
                  |  |?- †Stomiahykus
                  |  |-- †Chirodipterus
                  |  |-- †Conchodus
                  |  |-- †Dipteroides
                  |  |-- †Grossipterus
                  |  |-- †Pentlandia 
                  |  `-- †Dipterus
                  `--+?-o †Fleurantiidae
                     |  `-- †Fleurantia
                     `--+--o †Phaneropleuridae
                        |  |-- †Jarvikia
                        |  |-- †Nielsenia
                        |  |-- †Oervigia
                        |  |-- †Phaneropleuron
                        |  |-- †Scaumenacia
                        |  `-- †Soederberghia
                        |--o †Ctenodontidae
                        |  |-- †Ctenodus
                        |  `-- †Tranodis
                        `--+--o †Conchopomidae
                           |  `-- †Conchopoma
                           `--+--o †Uronemidae
                              |  `-- Uronemus
                              `--o Ceratodiformes
                                 |-- †Arganodus
                                 |-- †Gosfordia
                                 |-- †Microceratodus
                                 |-- †Paraceratodus
                                 |--o †Asiatoceratodontidae
                                 |  `-- †Asiatoceratodus
                                 |--o †Ptychoceratodontidae
                                 |  `-- †Ptychoceratodus
                                 |--o †Ceratodontidae
                                 |  `-- †Ceratodus
                                 |--o Neoceratodontidae
                                 |  |-- †Mioceratodus
                                 |  `-- Neoceratodus
                                 `--o Lepidosirenidae
                                    |-- †Gnathorhiza
                                    |-- Lepidosiren
                                    `-- Protopterus

Reference(s):

  • Carroll, R. L., 1988: Vertebrate paleontology and evolution.
    –W. H. Freeman and company, New York, 1988, 698.
  • Carroll, R. L., 1988: Appendix. 594-648.
    in Carroll, R. L., 1988: Vertebrate paleontology and evolution.
    –W. H. Freeman and company, New York, 1988, 698.
  • Cloutier, R. & Ahlberg, P. E., 1996: Morphology, characters, and the interrelationships of basal sarcopterygians.
    in Stiassny, M. L. J. et al., 1996: Interrelationships of Fishes.
    –Academic Press, San Diego, 1996, xiv-496

Reference(s):