According to these authors, the Pleidae derive from the Nepomorpha as a new heteropteran infraorder; the Plemorpha and the monophyletic infraorder Nepomorpha consist of five superfamilies with the following relationships: (Corixoidea + ((Naucoroidea + Notonectoidea) (Ochteroidea + Nepoidea)).
Two synapomorphies, that is, (5-7) and (33-5), have been found for the Notonectidae (Notonectoidea).
, the system of classification of the Nepomorpha included seven monophyletic superfamilies, namely, (Nepoidea, Corixoidea, Aphelocheiroidea, Naucoroidea, Ochteroidea, Notonectoidea, and Pleoidea (Pleidae + Helotrephidae)).
, on the basis of four Hox genes, supported the monophylies of the Nepomorpha, Naucoroidea (Aphelocheiridae + Naucoridae), Nepoidea (Belostomatidae + Nepidae), Ochteroidea (Ochteridae + Gelastocoridae), and Pleoidea (Pleidae + Helotrephidae); the Ochteroidea were the most basal lineage; the Notonectoidea contained Notonectidae only and formed a new sister relationship with the (Pleoidea + Naucoroidea) and the sister relationship with (Nepoidea + Corixoidea).
Actually, the clade Helotrephidae + Pleidae (Pleoidea) is also a sister group to the Notonectidae (Notonectoidea).
His scheme is similar to that of Rieger (1976) in the placement of Nepoidea [i.e., (Nepidae + Belostomatidae), see Schuh and Slater 1995:110] as sister group to the remaining Nepomorpha, and in having as the most derived clade the Notonectoidea
[i.e., (Notonectidae + (Helotrephidae + Pleidae))].
Previous studies strongly supported the view of separated superfamilies Notonectoidea
(including one family Notonectidae) and Pleoidea (including the Pleidae and Heloterphidae), recognized by China , Popov , Rieger , and Hebsgaard et al.