The skull is immovably fixed to the vertebral column. By far the greater part of the skeleton is cartilaginous. The notochord is persistent and unconstricted, its sheath is membranous, but cartilaginous neural and haemal arches are developed. Intercalary pieces (interdorsalia) occur between the neural arches, and similar pieces (interventralia) between the haemal arches. The cranium is covered with membrane bone, and teeth are but slightly developed. The tail is heterocercal. Gill rays occur on the hyoid arch, and the gills are protected by a bony operculum attached to the hyomandibular. The skin (1) may be almost or quite naked, (2) may carry bony plates arranged in rows, or may be covered (3) with rhomboidal scales, or (4) partly with rhomboidal, partly with cycloidal scales. _Suborder_ (2). CROSSOPTERYGII. The exoskeleton has the form of cycloidal or rhomboidal scales. The condition of the vertebral column differs in the different genera. Sometimes, as in _Polypterus_, there are well-developed ossified vertebrae; sometimes, as in many extinct forms, the notochord persists and is unconstricted. The tail may be diphycercal or heterocercal. The pectoral and sometimes the pelvic fins consist of an endoskeletal axis bearing a fringe of dermal rays. _Suborder_ (3). HOLOSTEI. The exoskeleton has the form of cycloidal or rhomboidal scales. The notochord is constricted and its sheath is segmented and ossified, forming distinct vertebrae, which are generally biconcave, sometimes opisthocoelous (_Lepidosteus_). The cartilaginous cranium is largely replaced by bone, and in connection with it we find not only membrane bone, but cartilage bone, as the basi-occipital, exoccipitals, and pro-otic are ossified. The tail is heterocercal. The suspensorium resembles that of Teleosteans, consisting of a proximal ossification, the hyomandibular, which is movably articulated to the skull and a distal ossification, the symplectic. The two are separated by some unossified cartilage. The cartilaginous upper and lower jaws are to a great extent surrounded and replaced by a series of membrane bones. _Order_ IV. TELEOSTEI.