"Being asleep can mean different things to different fish. Some fish and amphibians reduce their awareness but do not ever become unconscious like the higher vertebrates do. Fish have time periods when they become less aware of their surroundings but their brain waves do not change, and they do not exhibit REM sleep. They aren't quite asleep but they don't seem to be fully awake either."
found here
"Because sharks rely on ram-ventilation -- that is, their forward swimming to push oxygen-bearing water through their mouths and over their gills -- this fact begs the question: do sharks sleep at all? Dolphins are conscious breathers, actually having to think about rising to the surface, opening their blowholes, and breathing. From Russian studies carried out in the early 1970's, we know that dolphins catnap in 2 to 3-minute stretches, actually shutting down one hemisphere of their brain at a time. From experiments carried out on a small shark called the Spiny Dogfish (Squalus acanthias), we know that the 'Central Pattern Generator' that co-ordinates swimming movements in sharks is not located in the brain, but in the spinal chord. Thus, it is possible for an unconscious shark to swim. There is even a possibility that the sharks' fore, mid-, and hind- brain shut down in sequence, resulting in the shark equivalent of sleep-walking."
found here
