IntroductionThe hammerhead sharks, so named because of the unusual lateral expansion of the head, comprise a moderately large family of sharks occurring in tropical and temperate waters throughout the world.They are a rather old group; fossil remains have been found in Eocene deposits from Vu-ginia (Shelton P. Applegate, pers. comm.). The family belongs to the relatively speciose and poorly known suborder Galeoidea, in which are found most of the large and all of the dangerous kinds of sharks. Since the hammerheads are well defined, and, with one exception, adequate study material exists for all the species, they form an ideal taxon for systematic study.The most recent works of a revisionary nature that have appeared on the hammerheads (Tortonese, 1950, pp. 1-39; Fraser-Brunner, 1950, pp. 213-219) These ampullae, which are long canals filled with mucus, comprise a highly modified part of the lateral-line system, and it has been suggested that they may be involved in the detection of temperature changes, hydrodynamic pressure changes, tactile stimulation, and/or electric gradients (Young, 1962, p. 172). For brevity, these structures are referred to as mucal pores throughout this paper.Teeth vary according to species, although in several instances the differences are rather slight. Shape and arrangement of the teeth, as well as the presence or absence of serrations, are distinctive.There are differences between the species in size and shape of the fins and in the positions of these structures relative to each other.The positions of the foiu"th and fifth gill slits in relation to the insertion of the pectoral fin and the relative lengths of the gill slits are important.