Do fish go into REM sleep?

Answer 1

No. Most fish experience periods of rest which are analogous to sleep and can be defined as such. As noted above some fish (such as sharks) never physically rest and continuously move - however we have no way of knowing if this is automatic behaviour and the animals are sleeping while moving. We simply don't know.

However, fishes are not believed to experience REM sleep. Although they have analogues of the brain structures that are required for REM in mammals, there is no evidence to suggest that they have this feature.

In fact, a number of studies on reptiles have failed to provide evidence for REM sleep in them, suggesting it is very unlikely that an equivalent is present in fish.

Answer 2

I am aware of no research to prove or disprove that - however, I am aware that many fish do not sleep. Sharks, for example, never sleep.