Have you ever watched a dog taking a nap? As it sleeps, it may move its legs as if it wants to run. It may growl or even bark without waking up. When it acts that way, the dog is dreaming. What do you imagine a dog dreams about?

Scientists can't tell you what dogs -- or cats, or birds, or many other animals -- dream about. But they know that the animals, like human beings, dream. They can tell by watching what happens to the creatures' brain waves as they sleep.

Sleep and dream researchers use a special machine called an electroencephalograph, or EEG machine, to measure electrical signals from the brain. The EEG machine draws waves on a piece of paper. The waves stand for the amount of energy given off by the brain. By looking at the waves on the paper, a researcher can tell if the person is awake, sleeping deeply, or dreaming.

When a person is deeply asleep, the waves look long, like this:

When a person begins dreaming, the waves look shorter, like this:

A dreaming person's eyes move rapidly back and forth behind closed eyelids. This is the part of the night called REM sleep, for rapid eye movement. We dream between four and six times each night, but often we don't remember our dreams. By waking people up during their REM sleep, researchers have learned that everyone dreams -- and that all our dreams take place in color.

Dreams are like stories you tell yourself. You watch them, or even take part in them, as you sleep. Dreams are imaginary, but they're often about people or places that are familiar and important to you -- your school, your house, your friends, your family.

But dreams don't make sense the way the waking world does. In dreams, you may be able to fly. Your brother may turn into a cat. Your house may be in the middle of the ocean. In dreams, anything is possible. Sometimes, this makes dreams fun. At other times, dreams may be scary.

One scientist found that little kids, around 3 or 4 years old, had very simple dreams, often about animals. Older children's dreams get more complicated and last longer. They are usually very personal and involve family and friends. Often, the dreamer acts very grown up in the dream. Maybe these dreams are a way for kids to "rehearse" for life as an adult.

At one time or another, almost everyone has scary dreams, or nightmares. Young children, up to about age 10, may have them often. Very young children -- those under 6 -- may not be able to tell the difference between a dream and real life. A scary event in a dream, like seeing a monster under the bed, feels very real to them. This is perfectly normal, and most kids soon outgrow the feelings. When you were little, did you have nightmares, too?

Adults may have nightmares during times of tension or danger. Soldiers often have the scary dreams during wartime, for example. High fevers can also trigger nightmares.

If you do have a bad dream that leaves you feeling scared, try this trick. Let's say you had a dream in which you were being chased by a big bear. Next time you go to bed, tell yourself that if the bear appears again, you will climb a tree and be safe, or scare the bear away by making a loud noise. Remember that a dream is just a story -- and you're the storyteller.

Many doctors believe that people use dreams to work out strong feelings they have kept bottled up during the day.

Psychologists tell us that we need to dream. In some experiments, people who were awakened and deprived of their dream periods during the night soon became anxious and restless. But when they were allowed to sleep undisturbed, they had longer dream periods -- as if they were making up for the dreams they had missed.

Do you forget your dreams very quickly? Most people do. But sometimes a dream is very vivid when you first wake up. Try writing it down in a notebook by your bed as soon as you wake up. Share your dreams with your family -- you may end up learning some interesting things about yourself. Tips for Parents

These guidelines, adapted from Psychological Bulletin, may help relieve your child of the anxiety associated with frightening dreams:

* Develop a pleasant, soothing bedtime ritual. Try reading quietly together rather than roughhousing, which can make your child over-excited.

* Don't arbitrarily decide how much sleep your child needs. Watch his behavior, and gear sleeping hours to it.

* Use a neutral device to establish bedtime, like a particular hour on the clock, or the end of a special TV show. This can help avoid a personal struggle every evening.

* Make a distinction between bedtime and sleep time. Let your child go to bed, but allow her to play or read in bed until she's ready to sleep.

* Don't isolate your child. Leave the door open, play music in the living room, use a night-light. These devices can be reassuring, even for an older child.

* Don't allow your children to sleep in your bed. Psychologists counsel that letting a child sleep in the parents' bed prolongs the normal process of overcoming fear of separation.

* Talk with your child about dreams. This can help you find out what may be troubling him at home or at school.