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While the relationships of the extinct paleodictyopteroid orders (Diaphanopterodea, Paleodictyoptera, Megasecoptera, and Permothemistida) to each other and to other orders have not been extensively examined, the relationships of the three living lineages (Ephemeroptera, Odonata, and Neoptera) to each other have been the subject of much debate. Each of the three possible relationships are supported by various authors.

  

A monophyletic Paleoptera was advocated by Hennig (1969, 1981) and Hovmöller et al. (2002):

  

                   === Odonata      ==Paleoptera=| =====|            === Ephemeroptera      |      ================ Neoptera 

   

Boudreaux (1979) favored monophyly of Ephemeroptera + Neoptera:

  

      ====== Odonata      | =====|  === Ephemeroptera      ===|         === Neoptera 

     

Kristensen (1975, 1981, 1991) and Wheeler et al. (2001) present evidence in support of monophyly of Odonata + Neoptera:

  

      ====== Ephemeroptera      | =====|  === Odonata      ===|         === Neoptera