Flexi Says: There are three classes of fish: Class Agnatha (the jawless fish), Class Chondrichthyes (the cartilaginous fish), and Class Osteichthyes (the bony fish). All have the characteristics of fish in common, though there are differences unique to each class. Jaws, fins, and stomachs are absent in the jawless fish. Features of the jawless fish include a notochord, paired gill pouches, a pineal eye, and a two-chambered heart. The cartilaginous fish are jawed fish with paired fins, paired nostrils, scales, two-chambered hearts, and skeletons made of cartilage rather than bone. The bony fish are characterized by a lung or swim bladder, a cover over the gills, and bones covering the head and pectoral girdles.