A primitive order of ostariophysan fishes in which the first three vertebrae are specialized and associated with one or more cephalic ribs, thus representing a primitive Weberian apparatus (a series of bony ossicles that form a chain connecting the swim bladder with the inner ear). The order is further characterized by having the following features: an epibranchial (=suprabranchial) organ present, which consists of lateral pouches in the posterior part of the branchial chamber behind the fourth epibranchials; a small mouth and toothless jaws; no postcleithra and orbitosphenoid bones; and small parietal bones. The order comprises four families, treated below.