After Carroll, 1988, Gower, 1996, Frey, Sues & Munk, 1997, Gao & Fox, 1998, and Reisz, Modesto & Scott, 2011

<==o Neodiapsida Gauthier, 1984 sensu Benton, 1985
   |?-o †Weigeltisauridae Kuhn, 1936 [Coelurosauravidae Evans & Haubold, 1987] [transfered to a new basal diapsid group Avicephala by Phil Senter (2004)]
   |  |-- †Coelurosauravus elivensis Piveteau, 1926 [Daedalosaurus magagascariensis Carroll, 1976] U.Perm. CEu. Mad.
   |  |-- †Weigeltisaurus jaekeli (Weigelt, 1930) Kuhn, 1936 [Palaeochamaelo jaekeli Weigelt, 1930;; Gracilisaurus ottoi Weigelt, 1930; Coelurosauravus jaekeli (Weigelt, 1930) Evans & Haubold, 1987]
   |  `--o †Rautiania Bulanov & Sennikov, 2006; U.Perm. EEu.
   |     |-- †R. alexandri Bulanov & Sennikov, 2006
   |     `-- †R. minichi Bulanov & Sennikov, 2006
   |-- †Orovenator mayorum Reisz, Modesto & Scott, 2011
   `--+-- †Lanthanolania ivakhnenkoi Reisz & Modesto, 2003
      `--+-- †Apsisaurus witteri Laurin 1991
         `--o Eosuchia Broom, 1924 sensu deBraga & Rieppel, 1997
            |?=o †Eosuchia Broom, 1924 [Younginiformes Romer, 1945] [paraphyletic??, Rieppel, 1994 places these as basal lepidosauromorphs.]
            |  |?- †Acerosodontosaurus piveteaui Currie, 1980 [Acerosodontosauridae]
            |  |?- †Noteosuchus colletti (Watson, 1912) Broom, 1925 [Eosuchus colletti Watson, 1912] [preoccupied by Eosuchus lerichei Dollo, 1907, a gavialoid crocodylian]
            |  |-- †Galesphyrus capensis Broom 1914 [Galesphyridae Currie 1981]
            |  |--o †Younginidae Broom, 1914
            |  |  |-- †Heleosuchus griesbachi Broom 1913
            |  |  |-- †Thadeosaurus colcanapi Carroll, 1981
            |  |  `-- †Youngina capensis Broom, 1914 [Youngoides romeri, Youngopsis]
            |  `--o †Tangasauridae Haughton, 1924
            |     |-- †Hovasaurus boulei Currie, 1981
            |     |-- †Tangasaurus mennelli Currie, 1982
            |     `-- †Kenyasaurus mariakanensis Harris & Carroll, 1977
            `--+?- †Claudiosaurus germaini Carroll, 1981 [Claudiosauridae Carroll, 1981 ]
               |?-+--o †Lazarussuchus Hecht, 1992; U.Olig.-L.Mioc. Eu. [Lazarussaurus (lapsus calami)] [non-Choristodere sensu Gao & Fox, 2005]
               |  |  |-- †L. inexpectatus Hecht, 1992
               |  |  `-- †L. dvoraci Evans & Klembara, 2005
               |  `?- †Choristodera [alternative view after Gao & Fox, 1999]
               |?- †Ichthyosauromorpha Motani, Jiang, Chen, Tintori, Rieppel, Ji & Huang, 2014 (ichthyosaurs and relatives; kalaliskomaiset matelijat)
               `-- Sauria Gauthier, 1984 (uusmatelijat; modern diapsids)

Alternative phylogenies of basal neodiapsids:

After Bever, Lyson, Field & Bhullar, 2015:

<== Neodiapsida
   |-- †Hovasaurus
   `--+-- †Younginiformes
      `--+-- †Orovenator
         `--+-- †Claudiosaurus
            `--+-- †Kuehneosauridae
               `--o Sauria
                  |--+--+-- †Trilophosaurus
                  |  |  `-- †Rhynchosauria
                  |  `--+-- †Prolacerta
                  |     `-- Archosauriformes
                  `--+--+-- Rhynchocephalia
                     |  `-- Squamata
                     `--+-- †Acerosodontosaurus
                        `--+--o Pan-Testudinata
                           |  |-- †Eunotosaurus
                           |  `--+-- †Odontochelys
                           |     `-- †Proganochelys
                           `--+-- †Placodus
                              `--+-- †Sinosaurosphargis
                                 `-- †Eosauropterygia

Reference(s):

  • Bever, G. S., Lyson, T. R., Field, D. J. & Bhullar, B.-A. S., 2015: Evolutionary origin of the turtle skull.
    –Nature: in press [doi: 10.1038/nature14900]

After Motani, Jiang, Chen, Tintori, Rieppel, Ji & Huang, 2014:

<==o Sauria
   |--+--+-- †Helveticosaurus
   |  |  `-- †Choristodera
   |  `--o Lepidosauriformes
   |     |-- †Coelurosauravus
   |     `--+-- †Sophineta
   |        `--+--+-- †Pamelina
   |           |  `-- †Kuehneosauridae
   |           `--+-- Rhynchocephalia
   |              `-- Squamata
   `--+--+--+-- †Tanystropheus
      |  |  `-- †Macrocnemus
      |  `--+-- †Prolacerta
      |     `--+-- †Trilophosaurus
      |        `--+-- †Rhynchosauria
      |           `-- Archosauriformes
      `--+-- †Thalattosauriformes
         `--+-- †Wumengosaurus
            |-- †Ichthyosauromorpha
            `--o †Sauropterygia
               |--+-- †Largocephalosaurus
               |  `-- †Sinosaurosphargis
               `--+-- †Placodus
                  |-- †Pachypleurosauroidea
                  `--o †Eusauropterygia
                     |-- †Nothosauroidea
                     `-- †Pistosauroidea

Reference(s):

  • Motani, R., Jiang, D.-Y., Chen, G.-B., Tintori, A., Rieppel, O., Ji, C. & Huang, J.-D., 2014: A basal ichthyosauriform with a short snout from the Lower Triassic of China.
    –Nature: in press [doi: 10.1038/nature13866]

After Chen, Motani, Cheng, Jiang & Rieppel, 2014b:

<==o Neodiapsida(?)
   |-- †Tangasaurus
   |--+-- †Acerosodontosaurus
   |  `-- †Hovasaurus
   |--+-- †Youngina
   |  `-- †Thadeosaurus
   `--+-- †Claudiosaurus
      `--+--+-- †Thalattosauriformes
         |  `--+-- †Wumengosaurus
         |     `--+-- †Ichthyopterygia
         |        `--o †Hupehsauria
         |           |-- †Nanchungosaurus
         |           `-- †Hupehsuchus
         `--o Sauria
            |--o Archosauromorpha
            |  |-- †Choristodera
            |  `--+--+-- †Prolacerta
            |     |  `--+-- †Tanystropheus
            |     |     `-- †Macrocnemus
            |     `--+-- †Trilophosaurus
            |        `--+-- †Rhynchosauria
            |           `-- Archosauriformes
            `--o Lepidosauromorpha
               |--o Lepidosauriformes
               |  |-- †Helveticosaurus
               |  `--+--+-- †Pamelina
               |     |  `-- †Kuehneosauridae
               |     `--+-- Rhynchocephalia
               |        `-- Squamata
               `--o †Sauropterygia
                  |--+-- †Largocephalosaurus
                  |  `-- †Sinosaurosphargis
                  `--+-- †Placodus
                     `--+-- †Pachypleurosauroidea
                        `--o †Eusauropterygia
                           |-- †Nothosauroidea
                           `-- †Pistosauroidea

Reference(s):

  • Chen, X.-h., Motani, R., Cheng, L., Jiang, D.-y. & Rieppel, O., 2014b: The Enigmatic Marine Reptile Nanchangosaurus from the Lower Triassic of Hubei, China and the Phylogenetic Affinities of Hupehsuchia.
    –Plos One: Vol. 9, #7, pp. e102361 (1-13) [doi: 10.1371/journal.pone.0102361]

After Reisz, Modesto & Scott, 2011:

<==o Neodiapsida
   |-- †Orovenator
   `--+-- †Lanthanolania
      `--+--o †Tangasauridae Haughton, 1924
         |  |-- †Tangasaurus
         |  `--+-- †Hovasaurus
         |     `-- †Acerosodontosaurus
         `--+--o †Younginidae
            |  |-- †Thadeosaurus
            |  `-- †Youngina
            `--+-- †Claudiosaurus
               `-- Sauria

References:

  • Reisz, R. R., Modesto, S. P. & Scott, D. M., 2011: A new Early Permian reptile and its significance in early diapsid evolution.
    –Proceedings of the Royal Society of London B: Biological Sciences: Vol. 278, #1725, pp. 3731-3737 [doi: 10.1098/rspb.2011.0439]

After Ezcurra, Scheyer & Butler, 2014:

<==o Neodiapsida
   |-- †Coelurosauravus
   `--+--o †Younginiformes
      |  |-- †Acerosodontosaurus
      |  `-- †Youngina
      `--o Sauria
         |--o Lepidosauromorpha
         |  |-- †Paliguana
         |  |-- Rhychocephalia
         |  `-- Squamata
         `--o Archosauromorpha
            |--o †Protorosauria s.s.
            |  |--o †Protorosauridae
            |  |  |-- †Aenigmastropheus
            |  |  `-- †Protorosaurus
            |  `--o †Tanystropheidae
            |     |-- †Tanystropheus
            |     `-- †Macrocnemus
            `--+-- †Trilophosaurus
               `--+--+-- †Noteosuchus
                  |  `-- †Rhynchosauria
                  `--+-- †Prolacerta
                     `-- Archosauriformes

References:

  • Ezcurra, M. D., Scheyer, T. M. & Butler, R. J., 2014: The Origin and Early Evolution of Sauria: Reassessing the Permian Saurian Fossil Record and the Timing of the Crocodile-Lizard Divergence.
    –Plos One: Vol. 9, #2, pp. e89165 [doi: 10.1371/journal.pone.0089165]

After Bickelmann, Müller & Reisz, 2009:

<==o Neodiapsida
   |-- †Youngina
   |-- †Kenyasaurus
   |-- †Lanthanolania
   |-- †Thadeosaurus
   |-- †Galesphyrus
   `--+--+-- †Tangasaurus
      |  `--+-- †Hovasaurus
      |     `-- †Acerosodontosaurus
      `--+-- †Claudiosaurus
         `--+--+-- †Palaeagama
            |  `-- †Saurosternon
            `--+-- †Coelurosauravus
               `--o ?Sauria
                  |--+-- †Thalattosauriformes
                  |  `-- †“Ichthyosauromorpha”
                  `--+--o Lepidosauromorpha
                     |  |-- †Choristodera
                     |  `--+-- †Sauropterygia
                     |     `--+-- Testudinata
                     |        `--+-- †Kuehneosauridae
                     |           `-- Lepidosauriformes
                     `--o Archosauromorpha
                        |== †“Protorosauria”
                        `--+-- †Trilophosauria
                           `--+-- †Rhynchosauria
                              `-- Archosauriformes

References:

  • Bickelmann, C., Müller, J. & Reisz, R. R., 2009: The enigmatic diapsid Acerosodontosaurus piveteaui (Reptilia: Neodiapsida) from the Upper Permian of Madagascar and the paraphyly of “younginiform” reptiles.
    –Canadian Journal of Earth Sciencies: Vol. 46, pp. 651-661 [doi: 10.1139/E09-038]

After Müller, 2003

<==o Neodiapsida
   |-- †Younginiformes
   `--+-- †Claudiosaurus
      `--+-- †Kuehneosauridae
         `--+-- †Coelurosauravus
            `--+--+-- †Thalattosauriformes
               |  `-- †“Ichthyosauromorpha”
               `--o Sauria
                  |--o Lepidosauromorpha
                  |  |-- †Choristodera
                  |  `--+-- †Sauropterygia
                  |     `--+-- Testudinata
                  |        `-- Lepidosauriformes
                  `--o Archosauromorpha
                     |-- †Tanystropheus
                     `--+-- †Trilophosauria
                        `--+-- †Prolacerta
                           `--+-- †Rhynchosauria
                              `-- Archosauriformes

References:

  • Müller, J., 2003: Early loss and multiple return of the lower temporal arcade in diapsid reptiles.
    –Naturwissenschaften: Vol. 90, #10, pp. 473-476 [doi: 10.1007/s00114-003-0461-0]

Reference(s):