All mammals previously studied take maximal rest or sleep after birth, with the amount gradually decreasing as they grow to adulthood, and adult fruitflies and rats die if they are forcibly deprived of sleep. It has therefore been assumed that sleep is necessary for development and serves a vital function in adults. But we show here that, unlike terrestrial mammals, killer-whale and bottlenose-dolphin neonates and their mothers show little or no typical sleep behaviour for the first postpartum month, avoiding obstacles and remaining mobile for 24 hours a day. We find that neonates and their mothers gradually increase the amount of time they spend resting to normal adult levels over a period of several months, but never exceed these levels. Our findings indicate either that sleep behaviour may not have the developmental and life-sustaining functions attributed to it, or that alternative mechanisms may have evolved in cetaceans.