The porpoise, an air-breathing mammal whose habits are entirely aquatic, presents special problems of respiration, sleep, and anesthesia. These problems have been studied in three species, Tursiops truncatus, Lagenorhynchus obliquidens, and Phocoenoides dalli. The respiratory rhythm is unusual in that there is an extended pause-an apneustic plateau-between periods of expiration and inspiration. This rhythm has been observed under waking conditions, during sleep, and also when the animal is anesthetized. Two kinds of sleep behavior have been identified in Tursiops and Lagenorhynchus. In one of these, which is a light phase, the animal rests on the tank bottom for short periods, up to perhaps four minutes, and then comes to the surface to breathe. In a deeper phase the animal maintains itself at the surface for extended periods, breathing in an automatic fashion. In Phocoenoides no sleep behavior has been observed at any time.I have examined the special theory of Dr. John C. Lilly regarding respiration and sleep in the porpoise, which is based upon the assumption that respiration in this animal is altogether voluntary, and from my observations have concluded that respiration in the porpoise can be automatic or can be brought under voluntary control, just as in other mammals. Also the anesthetization of this animal can be carried out safely by methods that correspond closely to those employed in other animals.