Sleep spindles are a particular EEG wave detected in NREM sleep in healthy people. It gives information that the person is in the second phase of NREM sleep. When a sleep spindle is monitored on the EEG record, memory is being consolidated at that moment in the brain. Typically, this is supposed to happen during NREM sleep. When a sleep spindle is monitored during REM sleep, it indicates an abnormal condition called spindle REM sleep.
