supercohors Polyneoptera Martynov 
"Protorthoptera" Handlirsch, partim
cohors Dictyoptera Leach 
cohors Anartioptera Engel
magnordo Polyplecoptera novum 
(:10)
superordo Plecopterida Boudreaux
"Permoplecoptera"
Martynov
ordo Plecoptera
Burmeister
mirordo Mystroptera
Engel
ordo Zoraptera
Silvestri
ordo Embiodea
Kusnezov 
Embia
magnordo Polyorthoptera Engel & Grimaldi
superordo Dermapterida Boudreaux
"Protelytroptera"
Tyllyard, partim
ordo Dermaptera
De Geer
superordo Orthopterida Boudreaux
grandordo Notopterodea novum
(:10)
ordo Notoptera
Crampton 1915
fam. Tillyardembiidae Zalessky 1938 Tillyardembia
fam. Blattogryllidae Rasnitsyn 1976 Blattogryllus
Neonotoptera
Engel, novum
subordo Grylloblattodea Brues & Melander 1932
subordo Mantophasmatodea Zompro et al. In Klass et al. 2002, stat,nov. Mantophasma
grandordo Panorthoptera
Crampton
various
extinct stem group lineages
ordo Glosselytrodea
Martynov Glosselytron
ordo Caloneurodea
Handlirsch Caloneura
ordo Titanoptera
Sharov
ordo Orthoptera
Olivier
mirordo Holophasmatodea
Grimaldi & Engel
"Aeroplanoptera"
Tillyard
ordo Phasmatodea
Brunner van Wattenwyl Phasma