Sleep cycle

One sleep cycle typically consists of a period of NREM followed by a period of REM sleep.   The brain passes through four stages of NREM sleep first, going from light to deep sleep.  Then after coming back up to a brief period of shallow sleep, REM sleep begins.  Each sleep cycle lasts about 90 minutes, and in each successive cycle, the time spent in REM sleep increases and the time spent in NREM decreases.  Towards the end of an 8 hour night's sleep, the sleeper will alternate between REM sleep and the shallow stages of NREM, spending as much as an hour in REM sleep.

Sources:

Dement, The Promise of Sleep

Lavie, The Enchanted World of Sleep