The sleep cycle: A sleep cycle lasts about 90 minutes and during that time we move through five stages of sleep. The first four stages make up our non-rapid eye movement (NREM) sleep, and the fifth stage is when rapid eye movement (REM) sleep occurs.he sleep cycle: A sleep cycle lasts about 90 minutes and during that time we move through five stages of sleep. The first four stages make up our non-rapid eye movement (NREM) sleep, and the fifth stage is when rapid eye movement (REM) sleep occurs.