The Dermaptera are a small order of insects, marked by reduced forewings, hindwings with a unique and complicated folding pattern, and by pincer-like cerci. Hindwing characters of 25 extant dermapteran species are documented. The highly derived hindwing venation and articulation is accurately homologized with the other pterygote orders for the first time. The hindwing base of Dermaptera contains phylogenetically informative characters. They are compared with their homologues in fossil dermapteran ancestors, and in Plecoptera, Orthoptera (Caelifera), Dictyoptera (Mantodea, Blattodea, Isoptera), Fulgoromorpha and Megaloptera. A fully homologized character matrix of the pterygote wing complex is offered for the first time. The wing venation of the Coleoptera is re-interpreted and slightly modified. The all-pterygote character analysis suggests the following relationships: Pterygota: Palaeoptera + Neoptera; Neoptera: [Pleconeoptera + Orthoneoptera] + [Blattoneoptera + (Hemineoptera + Endoneoptera)]. Blattoneoptera share at least 15 wing apomorphies with the sistergroup Hemineoptera + Endoneoptera and none with the Orthoneoptera and Pleconeoptera; Blattoneoptera: (Grylloblattodea + (Dermaptera + Dictyoptera)); Dictyoptera: (Mantodea + (Blattodea + Isoptera). Dermaptera share 13 wing apomorphies with the sistergroup Dictyoptera. In order to document the intra-ordinal relationships of Dermaptera, 18 new characters of venation and articulation are added to an existing data set and analyzed cladistically. The following relationships are suggested (43 characters, tree length 72, CI 0.819 and RI 0.935). Dermaptera: Karschiellidae + ("Diplatyidae" + ("Pygidicranidae" + (Allostethus indicum + (Anisolabididae + ("Labiduridae" + [Forficulidae + (Chelisochidae + Spongiphoridae)]))))). The taxa in quotation marks are probably paraphyletic. Fossil Dermaptera and "Protelytroptera" show that wing-folding characters were already present in Permian ancestors. The evolution of the dermapteran wing-folding mechanism is discussed and the hindwing is presented as a working "origami" model, which will fold as in living earwigs. The functional role of the wing base in wing folding is examined. Characters in orders and other higher taxa are not independent and cannot be analyzed out of context with their groundplans. Higher systematics is dealing with diametrally different problems than species-level systematics. The necessity of using a different methodology for species-level and higher-level phylogenetics is discussed and recommendations are made.