[2] The subclass contains two orders, Psilotales and Ophioglossales, whose relationship was only confirmed by molecular phylogenetic studies.

Smith et al. (2006) carried out the first higher-level pteridophyte classification published in the molecular phylogenetic era, and considered the ferns (monilophytes), with four classes.

[2] Mark W. Chase and James L. Reveal (2009) classified them as two separate subclasses, Psilotidae and Ophioglossidae, corresponding to those orders within a much broader grouping, the class Equisetopsida sensu lato.

[1] The relationships between the two orders, Psilotales and Ophioglossales, has long been unclear and was only confirmed by molecular systematic studies.

[1] Equisetidae Ophioglossidae Marattiidae Polypodiidae The two orders, Ophioglossales and Psilotales are sister groups to each other.