What is REM? Unless you've ever specifically come across it in relation to sleep, you'll know REM as the band who sang 'Everybody Hurts'. But seriously what is REM? Rapid Eye Movement, it sounds more complicated than it really is. It's just a name that refers to the light phase of sleep. Babies spend 50% of thier time in REM sleep (that's why they make those cute jerky movements and eye flickets etc). If your baby was born prematurly he'll be in REM for closer to 80% of the time.
The non REM sleep is the really still part of sleep. The part that makes you wonder if they are still breathing. Totally normal as a 1st time mother to check on them the whole time during this part of the sleep. It's ok though you get over this after a while and if you don't the sensor pad is the way to go (look under best buys in my what to buy a new born).
By the 3rd month babies develeop a proper sleep pattern of 4 REM and non-REM sleep. Non-REM sleep has 4 STAGES. First they enter STAGE 1 of non-REM sleep (drowsy sleep) they quickly move into STAGE 2 (light sleep) and finally into STAGE 3 and STAGE 4 (very deep sleep). This whole cyle (STAGE 1-4) lasts 40-50mins. The baby then enters the REM sleep (which is a very light sleep) for 5-10mins and then back again into the non-REM cycle. This is why babies often wake up after 45mins, and if they don't know how to settle themselves back to sleep unassisted in that REM stage they wake up and the problems start. If they aren't able to get more than 40/50mins stretches during the day, by the afternoon they are super irritable and overtired and can't settle well into the night sleep. If you fall into the habit of assisting your baby back to sleep every 40/50mins you'll find yourself having to do that all the night as well.