Many hypotheses have been advanced to explain the adaptive significance of the sphyrnid cephalofoil, including potential advantages of spacing the olfactory organs at the distal tips of the broad surface. We employed comparative morphology to test whether the sphyrnid cephalofoil provides better stereo-olfaction, increases olfactory acuity, and samples a greater volume of the medium compared to the situation in carcharhiniform sharks. The broadly spaced nares provide sphyrnid species with a significantly greater separation between the olfactory rosettes, which could lead to an enhanced ability to resolve odor gradients. In addition, most sphyrnid species possess prenarial grooves that greatly increase the volume of water sampled by the nares and thus increase the probability of odorant encounter. However, despite a much greater head width, and a significantly greater number of olfactory lamellae, scalloped hammerhead sharks do not possess a greater amount of olfactory epithelial surface area than the carcharhiniform sandbar sharks. Therefore, sphyrnid sharks might not possess any greater olfactory acuity than carcharhinids. Despite this, there are clear olfactory advantages to the cephalofoil head morphology that could have led to its evolution, persistence, and diversification. J. Morphol. 264:253-263, 2005. © 2004 KEY WORDS: Carcharhinidae; Sphyrnidae; lamellae; nares; olfactory rosette; prenarial groove "…it would appear that the fish, by a sort of centrifugal action, go on shaking out the comparatively soft materials of the head more and more to the sides." (Kyle, 1926) The eight species of hammerhead sharks (Carcharhiniformes, Sphyrnidae) possess a head morphology that is unique among extant vertebrate taxa. Their name is derived from their dorsoventrally compressed and laterally expanded neurocranial morphology, which, when viewed dorsally, resembles a doubled-ended mallet or hammer. This peculiar cranial morphology has been termed the "cephalofoil" in recognition of its wing-like appearance (Compagno, 1984(Compagno, , 1988. Various hypotheses have been advanced to explain the function and adaptive significance of the cephalofoil but only a few have been empirically tested (Table 1). Several hypothetical sensory advantages have been ascribed to the cephalofoil including various perceived advances in olfactory capability. The olfactory hypotheses fall into three categories: 1) enhanced olfactory klinotaxis, 2) increased olfactory acuity, and 3) larger sampling swath of the surrounding medium.To put these hypotheses into a quantifiable context, consider the probability that an odorant molecule binds to a receptor in the nasal rosette. The number of odorant molecules that cross the olfactory epithelium is:where C is the concentration of odor molecules, A n is the area sampled by the naris, and V is the velocity of odorant over the olfactory rosette (Fig. 1). The stimulus strength (S) is:where the number of receptors is assumed to be proportional to the area of the sensory epithelium (A r ), and t is...