"Please, Mom, please let me stay up!" you beg. There's a late show on TV that you really want to see.

Your mother says you may stay up and watch. At first, it's a lot of fun sitting in the living room late at night, when you'd usually be fast asleep.

The monster movie is pretty exciting. But before long, your eyelids start to droop. Your head nods forward. Your legs give a little twitch. When your mother comes in to check on you, she finds you "dead to the world" in front of the flickering television.

What happened? In spite of yourself, you fell asleep. Your body knew it was bedtime, even though your mind tried to tell it to stay awake just this once.

Human beings need to sleep in order to stay healthy. Sleep refills you with energy and gives your brain and nervous system a rest. Scientists have found that people who go without sleep get short-tempered. They lose their ability to concentrate. They forget things. After a while, they actually start falling asleep on their feet. One researcher in Sweden walked his subjects through the streets of a city after they had been awake for a few days. The scientist noticed that the sleepy people's eyes actually closed as they were walking. They took short naps even though they were standing upright.

If there is a baby in your house, you know that infants need a lot of sleep. Most babies sleep about 14 hours out of each 24. They do this by taking lots of naps. Preschoolers usually sleep 12 to 14 hours during each 24-hour day. School-age kids need between 10 and 12 hours of sleep.

Most adults, on the other hand, feel just fine after about seven or eight hours of sleep each night. But not all people have the same needs. Some can get by on only a few hours, with brief naps thrown in for refreshment. Other adults need 10 or 12 hours of sleep. As you grow up, your body will let you know how much sleep it requires to stay in tip-top order.

After you fall asleep, your body rests. Your heart keeps beating, but it slows down. Your brain "turns off" and stops responding to most of the things that are happening. A loud noise like an alarm clock can wake you -- but other noises go unheard. You are no longer aware of what is going on around you.

Scientists use a device called an electroencephalograph, or EEG machine, to measure the electric impulses in the brain. In a painless procedure, they attach wires to someone's forehead, and chart the electricity his brain gives off as he sleeps. Using this method, scientists learned that people pass through different stages of sleep every night.

The first stage of light sleep lasts only a few minutes. If someone wakes you up during this time, you may not feel like you were really asleep at all. Has that ever happened to you?

Next, your body passes into deeper and deeper sleep. After about an hour and a half, you reach the deepest stage. You breathe regularly; your heart pumps slowly. Your muscles rest. Your eyes are unfocused and motionless behind their closed lids. Then something happens. Your eyes starts to move back and forth, as if you were awake and watching a tennis match. Your heart rate and breathing rate become uneven. Your body may toss and turn. During this stage, called REM for "rapid eye movement," you have the most vivid dreams of the night. After a time, the REM stage ends, and you go back to quiet sleep without eye movement.

Most people go through several REM periods every night. By the time you wake up in the morning, about one-quarter of your night has been spent in dreaming. The other three-quarters, your body rested.

Scientists still don't know all about sleep. For example, they still haven't found out exactly what kinds of chemicals make you go from being awake to being asleep. They do know that you need both REM and quiet sleep to keep you well. Some experiments show that a chemical you need to make you grow is released during REM sleep. And dreams help you think about feelings and fears that build up during the day. You can learn more about dreams on this page next week.

In the meantime, sleep well. It may sometimes feel like a waste of time, but sleep is a very important part of being alive. After all, if you count all the time you spend sleeping in your life, it will probably add up to about 20 years. Tips for Parents -------

When otherwise healthy children begin to have sleep problems, it's time to take notice. According to a study conducted a two hospitals in Cleveland, such behavior as bedtime struggles and night waking may indicate daytime distress. The results of the study appear in this month's issue of the journal Pediatrics.

Stressful situations that may cause sleep problems include:

* An accident or illness in the family.

* Unaccustomed absence of the mother.

* Parental depression.

* Sleeping with parents.

The researchers concluded that disturbances of sleep patterns that last for more than a month may indicate potentially important problems. Lengthy periods of such behaviors as protesting bedtime for more than an hour, waking parents many times during the night, or refusal to allow parents to leave the room may indicate that it's time to consult a health professional to determine the nature of the child's stress, and help combat it effectively.