Relationships among families referred to the superfamily Diopsoidea (or Nothyboidea) are discussed from the evidence of comparative morphology, particular attention being given to the Nothybidae, Psilidae, Syringogastridae, and Diopsidae. Some comments are made on selection of autapomorphies in cladistic methodology. The Tanypezidae and Somatiidae are removed from the Diopsoidea to incertae sedis. The new diopsoid family Gobryidae, or hinge flies, is established for the Oriental-Australasian genus Gobrya Walker, previously variously associated with the families Megamerinidae, Nothybidae, and Syringogastridae. A key to the families which have been included in Diopsoidea is given. A systematic arrangement of taxa mentioned in the discussion is appended.