The name Palaeoptera has been traditionally applied to those primitive groups of winged insects (most of them extinct) that lacked the ability to fold the wings back over the abdomen as characterizes the Neoptera. The complexities of the wing-folding mechanism, as well as the mechanical operation of the wings in flight (indirect flight muscles), are such that it clearly indicates the Neoptera are a monophyletic lineage. The Diaphanopterodea, which are palaeopteran insects, had independently and uniquely evolved a different wing-folding mechanism.

The problem is that the plesiomorphic absence of wing-folding does not necessarily mean the Palaeoptera form a natural group – they may simply be an assemblage containing all insects, closely related or not, that "are not Neoptera", an example of a wastebasket taxon. As it stands, the relationship of the two living Paleopteran groups – Ephemeroptera (mayflies) and Odonata (dragonflies and damselflies) – to the Neoptera has not been resolved yet; there are three competing main hypotheses with many variations. In two of these – those that treat the ephemeropteran or the odonatan lineage as closer to the Neoptera than to the other "palaeopterans" – the Paleoptera appear to be paraphyletic and thus an artificial grouping that is best abandoned.