An order of liverworts in the subclass Marchantiidae, consisting of two families, the terrestrial Sphaerocarpaceae (Sphaerocarpos and Geothallus) and the aquatic Riellaceae (Riella). The plants are characterized by envelopes surrounding each antheridium and archegonium, absence of elaters, poor development of seta, and absence of thickenings in the unilayered wall of an indehiscent capsule.