Coleorrhyncha or Peloridiomorpha, also known as moss bugs or beetle bugs, are a suborder of Hemiptera and represent an ancient lineage of moss-feeding insects that evolved in the southern paleo-continent Gondwana. They show some similarities to the Heteroptera but have been considered distinct. It has a single extant family, the Peloridiidae. Three other families have been established on the basis of fossils and these include the more ancient (Later Permian to Jurassic) Progonocimicidae and the later Karabasiidae and Hoploridiidae. The Coleorrhyncha were earlier included within the "Homoptera" but based on studies of their morphological similarities as well as molecular phylogeny are now considered as a sister group of the Heteroptera. They have wings in some species which are reduced in others but all species are flightless and live in damp moss habitats and are associated with the distribution of Nothofagus trees in Australia, New Zealand, New Caledonia, and South America.
The fossil family Progonocimicidae was formerly considered as early Heteroptera or survivors from a stem group of Heteropteroides but based on morphology, Popov called them an ancestral sub-group of the Coleorrhyncha, and this has been followed by subsequent authors.
In 2013 a new species of Progonocimicidae, the fossil species, Cicadocoris assimilis, was discovered in rocks of the Middle Jurassic in China. It was found in the Jiulongshan Formation in Daohugou Municipality, Ningcheng County, Inner Mongolia. Previously reported as Cicadocoris Becker-Migdisova, 1958, and Mesocimex Hong, 1983, it had not been placed in the Progonocimicidae.