†class Psilophytopsida Kidston and Lang 1917
Synonym: Trimerophytopsida Foster and Gifford 1974
Parent taxon: Psilophytophyta according to A. B. Doweld 2001
Sister taxa: Acanthophyton, Arthrostigma, Barrandeina, Drepanophycus, Eogaspesiea, Hedeia, Hicklingia, Himantophyton, Hornea, Horneophyton, Hostinella, Niayssia, Polyxylon, Psilodendrion, Psilophytites, Psilotiphyllum, Reimannia, Reimanniopsis, Serrulacaulis, Stolbergia, Svalbardia, Taeniocrada, Tomiphyton
Subtaxa: Dawsonites Psilophytales