Head rounded; forehead rather convex. Teeth conical; of upper jaw early deciduous, of lower jaw only in the front over the short symphysis. Dorsal fin low, rather behind the middle of the back. Pectoral fins ovate, elongate. Skull depressed, with the lateral expansions horizontal, rather thickened and bent up over the orbit and slightly dilated and bent down over the notch. Intermaxillaries dilated, swollen in front of the blower. Atlas free; rest of cervical vertebræ and dorsal processes united. The arm-bones short. Two middle fingers elongated, subequal, of eight or nine phalanges; the other fingers very short, of two or three phalanges. The breast-bone single, broad in front. 1. GRAMPUS. Grampus, _Gray_, _l. c._ pp. 230, 295, 393; _Synops. Whales & Dolph._ p. 9. † _Triangle in front of the blowers elongate, produced in front over the vomer. Bladebone triangular, the height about two-thirds the width. Beak of skull narrow, more contracted for two-thirds of its length._ 1. Grampus Rissoanus. Grampus Rissoanus, _Gray_, _Cat. Seals & Whales_, p. 298; _Gervais_, _Ostéog. Cét._ t. 54. figs. 1-6; _Murie_, _Journ. Anat. & Physiol._ 1870, v. p. 129, t. 5 (good). Beak of skull rather broad or gradually tapering towards the front; intermaxillaries rather broad; bladebone triangular, the height three-fourths the width. Inhab. Nice. 2. Grampus Cuvieri. B.M. Grampus Cuvieri, _Gray_, _l. c._ p. 295, fig. 60; _Synops. Whales & Dolph._ p. 9. Grampus griseus, _Gervais_, _Ostéog. Cét._ t. 54. figs. 1-6. Inhab. North Sea, Hampshire. †† _Triangle in front of the blowers short, broad._ 3. Grampus Richardsonii. Grampus Richardsonii, _Gray_, _l. c._ p. 299; _Synops. Whales & Dolph._ p. 9. Inhab. Cape of Good Hope. Family 12. GLOBIOCEPHALIDÆ. Globiocephalidæ, _Gray_, _l. c._ pp. 62, 313; _Synops. Whales & Dolph._ p. 8. Head blunt, very much swollen. Teeth in the front part of both jaws, cylindrical, simple; symphysis very short, shorter than the tooth-line. Dorsal fin falcate. Pectoral fin low down on the sides of the body; fingers elongate, many-jointed. Atlas and the rest of cervical vertebræ united, or the hinder one free. Scapula triangular, with large coracoid and acromion processes. Arm-bones very short. Metacarpal bones in cartilage. The two middle fingers very long, of twelve to ten joints; the rest of the fingers short, of three or four phalanges; index finger short, slender, four-jointed; ring-finger shorter, three-jointed; little finger very short, of one phalange. Breast-bone of three separate pierced pieces; the hinder one narrow. 1. GLOBIOCEPHALUS. Globiocephalus, _Gray_, _l. c._ p. 313; _Synops. Whales & Dolph._ p. 8. Skull:—palate flat; beak rather tapering in front. First to sixth cervical vertebræ anchylosed into one mass, seventh free. Vertebræ 58 or 59:—C. 7. D. 11. L. and C. 40 or 41.