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 ambhibians. 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 Ahlberg, 1995
   |  |-- †Elginerpeton pancheni Ahlberg, 1995
   |  `-- †Obruchevichthys gracilis Vorobyeva, 1977
   `--+?- †Densignathus rowei Daeschler, 2000
      |--+?- †Metaxygnathus denticulus Campbell & Bell, 1977
      |  `-- †Ventastega curonica Ahlberg et al., 1994 [Panderichthys bystrovi Gross, 1941, in partim]
      `--+?- †Sinostega pani Zhu, Ahlberg, Zhao & Jia, 2002
         |-- †Acanthostega gunnari Säve-Söderbergh [Acanthostegidae]
         `--+?- †Ymeria denticulata Clack, Ahlberg, Blom & Finney, 2012
            |--o †Ichthyostegidae sensu Blom, 2005
            |  |-- †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
               |?- †Ossinodus pueri Warren & Turner, 2004
               `--+--o †Whatcheeriidae Clack, 2002
                  |  |-- †Whatcheeria deltae Lombard & Bolt, 1995
                  |  `-- †Pederpes finneyae Clack, 2002
                  `--+-- †Crassigyrinus scoticus Watson, 1926 [Crassigyrinidae]
                     `--+-- †Eoherpeton watsoni Panchen, 1975 [Eoherpetontidae]
                        `--+-- †Emblomeri s. s.?
                           `--+-- †Gephyrostegida
                              `--o Tetrapoda sensu stricto?
                                 |--+-- †Westlothiana lizziae Smithson & Rolfe, 1990
                                 |  `-- Lepospondyli von Zittel, 1887 [incl. Gymnophiona sensu Anderson et al., 2008]
                                 `--+== Reptiliomorpha Säve-Söderbergh 1934?? (vesikalvollismaiset tetrapodit; amniote-like tetrapods)
                                    `--+-- Temnospondyli Zittel, 1888 sensu Laurin & Reisz, 1997 [incl. Batrachia sensu Anderson et al., 2008]
                                       `--+-- †Colosteoidea
                                          `-- †Baphetoidea Cope, 1875 [Loxommotoidea]

Stegocephali incertae sedis:

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

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

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

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

Reference(s):