The trick of keeping half the brain continuously awake is vital to their survival, scientists believe.
It allows them to come to the surface every so often to breath, and remain constantly vigilant for sharks.
Scientists in California tested the ability of two bottlenose dolphins -- a male called Nay and female called Say -- to echo-locate accurately over periods of time that would have left other animals sleep-deprived.
Lead researcher Dr Brian Branstetter, from San Diego, said: "The demands of ocean life on air-breathing dolphins have led to incredible capabilities, one of which is the ability to continuously, perhaps indefinitely, maintain vigilant behaviour through echolocation."
Brain wave measurements have confirmed that the creatures are capable of 'unihemispheric sleep'. When dolphins sleep in this way, they often keep one eye open.