Note:

Phylogeny of basal tetrapods [amphibians] is quite murky. This murkiness focuses greatly in the question of the origin and relationships of modern amphibians.

Carroll (1988) presents view that modern amphibians [Lissamphibia] is a polyphyletic group, gymnophionas and salamanders being advanced microsaurs and frogs being advanced temnospondyls. Milner (1994) in the other hand, presents a view of monophyletic Lissamphibia, which sistergroup are plagiosaur-dissorophoids. Laurin & Reisz (1997) support view, in which lissamphibians belong to reptiliomorphs. Yates & Warren (2000) present a comprehensive phylogenetic analysis of Temnospondyli, but it didn't include lissamphibians.

Most recently Anderson et al. (2008), while describing a new Amphibamid temnospondyl, and after running a phylogenetic analysis, came to a conclusion, that the Batrachia (i.e. frogs and salamanders where close relatives of this new amphibamid and thus belonged to the temnospondylian amphibians. In the same analysis they also found that gymnophiones share a most recent ancester with microsaurs of the lepospondylian amphibians. Based on their new phylogeny they resurrected Carroll's idea of polyphyletic origin of Lissamphibia.

After Clack, 2002

Alternative phylogeny of basal Tetrapoda after Carroll (1988), Milner (1994) and Clack (1998)

Alternative phylogeny of basal Tetrapoda after Laurin, 1996-2001 [“The Tree of Life”]

<==o Stegocephali Cope, 1868 sensu Laurin, 1998a [Tetrapoda Haworth, 1825 sensu Goodrich 1930 and Laurin & Reisz, 1997; Tetrapodamorpha Ahlberg, 1991] (tetrapods = vertebrates with four recognizible limbs; maaselkärankaiset)
   |--o †Elginerpentonidae
   |  |-- †Elginerpeton pancheni Ahlberg, 1995
   |  `-- †Obruchevichthys gracilis Vorobyeva, 1977
   `--+?- †Densignathus rowei Daeschler, 2000
      |--+?- †Metaxygnathus denticulus Campbell & Bell, 1977
      |  `-- †Ventastega curonica Ahlberg, Luksevics & Lebedev, 1994 [Panderichthys bystrovi Gross, 1941, in partim]
      `--+?- †Sinostega pani Zhu, Ahlberg, Zhao & Jia, 2002
         |-- †Acanthostega gunnari Säve-Söderbergh [Acanthostegidae]
         `--+--o †Ichthyostegidae
            |  |-- †Ichthyostegidae gen. et sp. indet. [U. Dev. WEu. (Belgium)] [Clément et al., 2004]
            |  `--o †Ichthyostega Säve-Söderbergh, 1932 [taxonomic history]
            |     |-- †I. stensioi Säve-Söderbergh, 1932 Säve-Söderbergh, 1932 [taxonomic history]
            |     |-- †I. eigili Säve-Söderbergh, 1932 [taxonomic history]
            |     `-- †I. watsoni Säve-Söderbergh, 1932 [taxonomic history]
            `--+-- †Hynerpeton bassetti Daeschler, Shubin, Thomson & Amaral, 1994
               `--+--o †Whatcheeriidae Clack, 2002
                  |  |-- †Whatcheeria deltae Lombard & Bolt, 1995
                  |  `-- †Pederpes finneyae Clack, 2002
                  `--+-- †Crassigyrinus scoticus [Crassigyrinidae]
                     `--+-- †Eoherpeton watsoni Panchen, 1975 [Pholidogaster pisciformis Watson, 1929] [Eoherpetontidae]
                        `--+-- †Emblomeri s. s.?
                           `--+-- †Gephyrostegida
                              `--o Tetrapoda sensu stricto? [the last common ancestor of modern amphibians and amniotes]
                                 |--+-- †Westlothiana lizziae Smithson & Rolfe, 1990
                                 |  `-- Lepospondyli [incl. Gymnophiona sensu Anderson et al., 2008]
                                 `--+-- †Reptiliomorpha?? (vesikalvollismaiset tetrapodit; amniote-like tetrapods)
                                    `--+-- Temnospondyli Zittel, 1888 sensu Laurin & Reisz, 1997 [incl. Batrachia sensu Anderson et al., 2008]
                                       `--+-- †Colosteoidea
                                          `-- †Baphetoidea [Loxommotoidea]

Stegocephali incertae sedis:

Antlerpeton clarkii Thomson, Shubin & Poole, 1998
    †Sigournea multidentata Bolt & Lombard, 2006
    †Occidens portlocki Clack & Ahlberg, 2004

After Danto, Witzmann & Müller, 2012

<==+-- †Acanthostega
   |--+-- †Ventastega
   |  `--+-- †Panderichthys
   |     `-- †Eusthenopteron
   `--+-- †Ichthyostega
      `--+-- †Tulerpeton
         `--+--+-- †Greererpeton
            |  `-- †Colosteus
            `--+-- †Crassigyrinus
               `--+-- †Whatcheeria
                  `--+-- †Baphetoidea
                     `--o Tetrapoda
                        |--o Batrachomorpha
                        |  `-- Temnospondyli [incl. Lissamphibia]
                        `--o Reptiliomorpha
                           |-- †Emblomeri
                           `--+==Gephyrostegida
                              `==o †Seymouriamorpha
                                 |-- †Discosauriscidae
                                 `--+-- †Seymouriidae
                                    `--+-- †Kotlassiidae
                                       `--+--+-- †Westlothiana
                                          |  `--+-- †Solenodonsaurus
                                          |     `-- †Lepospondyli
                                          `--o Cotylosauria
                                             |-- †Diadectomorpha
                                             `-- Amniota

Reference(s):

  • Danto, M., Witzmann, F. & Müller, J., 2012: Redescription and phylogenetic relationships of Solenodonsaurus janenschi Broili, 1924, from the Late Carboniferous of Nırany, Czech Republic.
    –Fossil Record: Vol. 15, #2, pp. (45-59) [doi: 10.1002/mmng.201200003]

After Laurin, 1996-2001 ["The Tree of Life"]

<==o Stegocephali
   |--o †Elginerpentonidae
   |  |-- †Elginerpeton
   |  `-- †Obruchevichthys
   `--+?- †Densignathus
      |--+?- †Metaxygnathus
      |  `-- †Ventastega
      `--+-- †Acanthostega
         `--+-- †Ichthyostega
            `--+-- †Hynerpeton
               `--+--o †Whatcheeriidae
                  |  |-- †Ossinodus
                  |  `--+-- †Whatcheeria
                  |     `-- †Pederpes
                  |-- †Crassigyrinus
                  `--+-- †Baphetoidea
                     `--o Tetrapoda sensu stricto
                        |-- Temnospondyli
                        `-- Reptiliomorpha

After Carroll, 1988, Milner, 1994, and Clack, 1998

<==o Tetrapoda
   |--o †Elginerpentonidae
   |  |-- †Elginerpeton
   |  `-- †Obruchevichthys
   `--+?- †Densignathus
      |--+?- †Metaxygnathus
      |  `-- †Ventastega
      `--+-- †Acanthostega
         `--+-- †Ichthyostega
            `--+-- †Hynerpeton
               |?- †Antlerpeton
               `--+?-+?-o †Adelogyrinidae
                  |  |  |-- †Adelogyrinus
                  |  |  |-- †Adelospondylus
                  |  |  |-- †Dolichopareias
                  |  |  `-- †Palaeomolgophis
                  |  |?- †Acherontiscus
                  |  `?- †Aistopoda
                  `--+?-o †Whatcheeriidae
                     |  |-- †Ossinodus
                     |  `--+-- †Whatcheeria
                     |     `-- †Pederpes
                     |?- †Nectridae
                     `--o Tetrapoda sensu stricto
                        |-- Batrachomorpha
                        `--+-- †Baphetoidea
                           `-- Reptiliomorpha

Reference(s):