Sperm whales literally drift off to sleep for short periods, according to researchers at St Andrews University.
After studying the mammals, they found that whales "cat nap" for short bursts and end up drifting through the water.
Scientists who tagged 59 whales in various locations around the world have recorded them performing slow vertical "drift dives" as they sleep.
It is thought the research shows that sperm whales sleep much less than any other mammal on land or sea.
The whales were recorded consistently performing the dives in each location which the study suggested indicated it was stereotypical for the entire species.
Video footage showed six sperm whales eerily floating vertically in a motionless manner, with their heads either at or just below the surface of the sea.
Researchers said three of them were "unusually non-responsive" to the approaching boat, until it accidentally touched one of them.
Dr Patrick Miller, from the school of biology's sea mammal research unit, said: "Many mammals show species-typical sleeping behaviour, such as dogs circling before lying down, lending support to the idea that sperm whales sleep during these drift dives.
"The sperm whale behaviour we describe seems to allow normal-looking quiescent sleep, possibly including REM sleep, which has never been clearly observed in any cetacean.
"Reduced responsiveness that reverses with sufficient stimulation to cause waking is another important criteria that allows us to consider this to be a sleeping behaviour."
The researchers believed that the video also seemed to show that the whales were asleep with both eyes shut.
Previous studies of captive dolphins has suggested that cetaceans - including whales, dolphins and porpoises - sleep with one side of the brain at a time.
The data, gathered over 562 hours, also revealed that such whales appeared to sleep for just 7.1% of the time, most often between 1800 and midnight.