THREE-YEAR-OLD Kay had an imaginary playmate simply called "Girl Friend," whom she controlled rigidly but gently. When Irene was 4, a delightful, fut invisible, old lady named Mrs. Scrippidux was her constant companion.

And Mark, at 2 1/2, invented a friend, incredibly called Bockbeer. Being part bear and part person, this quasi animal became a delightful tool with which young Mark could manipulate neighborhood kids who believed in Bockbeer as firmly as did Mark. This is the way it goes with those marvelous creations of your child's imagination, with no restrictions as to sex, age, or country of origin.

Often an only child, lacking the companionship of a brother or sister, will tend to invent a friend to keep him company during his hours alone. Or perhaps the youngest in the family, when the older children return to school in September, suddenly takes on an invisible playmate.

For the most part, your child's imaginary friends are nothing to be concerned about. Psychologists are almost in complete accord regarding the causes and effects of the phenomenon, and they are almost always benign. Sometimes, according to Ann Horton, a Fairfax psychiatric social worker, when a new baby shows up in the family, a new invisible friend shows up simultaneously. But, as a rule, as suddenly and as unexpectedly as the mythical individual arrives, just as suddenly does he vanish.

My first experience with the imaginary friend started one day when my first child was about three years old. I was expecting a new baby in October and perhaps in those long summer months before the arrival, Greg was preparing himself to share his life with the newcomer. Suddenly one day -- not one, not two, but three imaginary friends popped into the picture.

"Mommy," Greg called as he trooped up the basement steps, "can I have someone for lunch?"

"Of course," I replied, thinking he meant the youngster down the street.

But in he came, completely alone. Or so I thought.

He introduced them with a flourish, pointing to each of them as he spoke his name. "This is Lum Lum," he said, "and this is Lei Lum, and this is Mary Ann." Later my husband was to ponder how Mary Ann got mixed up with this Polynesian group; but ours not to reason why, or how, names are bestowed on the fanciful crations of our children's minds.

I accepted the introduction, invited them all to lunch, and thought that would end the matter. But Greg was a stickler for propriety. He turned to them deferentially.

"I'm having a tomato sandwich, Lei Lum," he said. "Would you like a tomato sandwich? We also have peanut butter and jelly. And, Mary Ann, what would you like? Lum Lum?"

How difficult the processes of the imaginary playmate become, depends upon the degree of minutes to which your child subjects you in his demands for himself and the playmate. Thank heaven Greg didn't demand multiple sandwiches actually to be prepared. Looking back on it now, the imaginary process would have been shattered if the reality of a phalanx of un-eaten sandwiches stared us in the face during our conversational little lunch. The pretend part is fun and the family should never be so caught up in the aesthetics of the situation that they might begin to treat it as real.

In Elizabeth Post's "Please, Say Please," the author cautions" . . . mother should make it very clear that she accepts and recognizes the existence of the imaginary character, but only as fiction. She knows, and she assumes her child knows, the image is not real."

No corner-cutting, however, was to be tolerated insofar as operations were concerned, and I found myself going through the complete pantomine of preparing three imaginary sandwiches, spreading mayonnaise, sprinkling salt, pouring milk, serving up the padding, and even being cautioned about specific peccadillos of this choosy little band. Mary Ann, for example, didn't like butter, and Lum Lum preferred catsup instead of mayonnaise.

"He's weird," Greg said to me in an aside.

Once Mary Ann spilled her milk and I had to wipe up an imaginary puddle.

Later at nap time, I pulled a boo boo. Greg got in bed, rolled way over to the wall side and I sat down, only to be rudely brought to my senses by my son, aghast at my lack of sensitivity.

"Hey! Watch it! GReg admonished. "You're sitting on Mary Ann."

How long the three interlopers actually stayed with us, I don't remember. I do remember that we had them around for a good portion of the summer. They shared Greg's bed, his bath, and his board. They drove me bananas with their omnipresence. And then they were gone, never to return.

"Creating a fantasy companion," says Horton, "is a child's creative way of dealing with loneliness. Yet he builds a vivid fantasy only to endow it with the most rigid rules." Strict behavioral patterns are bestowed on the friends and no one deviates from one's expected code of behavior or type of response. In the case of our Polynesian group, for example, Lei Lum was unfailingly loyal, pleasant, and well-behaved, while Mary Ann was a lovable but rather inept little girl who required a great deal of encouragement and appreciation. (Even at 3, my son, I must admit, had, somehow, latched on to an unfortunate stereo-type.) In contrast to these two, Lum Lum, quite obviously the scapegoat of whatever irritations may have troubled our son that summer, was the villian of the group. Greg obviously disliked him and gave him short shrift.

Part of the fun of creating one's own companions, of course, is that they can be whatever the creator wants them to be. Occasionally a child will create a companion to bear the brunt of his own misdeeds. I knew a little boy years ago whose name was Emil and who had introduced Good Mull and Bad Mull into the family circle.He used them only to attribute his own deeds to -- both good and bad. But, according to Horton, there was strength in owning a shadowy side. "The particular boy built up a bad side and then disowned it. He could view the bad behaviour as an outsider and deal with it more effectively.

"Only if it goes on too far into later life can it be dangerous," she continued. "Yet it's a cue for parents to pick up on, and they should take into context other things that are going on in terms of determining whether it's a problem or not and then evaluating it."

This opinion was echoed by Eileen Burnet, special education teacher in the Alexandria public schools. "It's all part of the development process," said Burnet. "The imaginary playmate is a healthy fantasy and parents should not treat it as strange or abnormal. Sometimes in large families a middle child will create these illusionary companion, these docile individuals that the youngster can dominate."

Burnet also spoke of the creativity involved in a child who invents his own friends. "It's all part of the pretend world," she said, "and it's a healthy outlet for loneliness."

An interesting aspect of the imaginary game is the similarity of the names the child gives his people when they are invented in groups, as is witnessed by our own Lum Lum and Lei Lum.

One mother I spoke with told me of Gaka, Gakatiti, and Gaka Kume Bless, a group her 3-year-old had invented a few years ago when the family was transferred to France. Several other children in the family had kept him company for the first few weeks of their tour of duty, but when fall came the older ones went to school and left Michael alone with only French-speaking neighbors to play with. And then one day he was part of his thriving imaginary crew.

Gaka arrived first, a rollicking, devil-may-care bravado who dreamed up all manner of exciting activity. the two boys had a great time together and suddenly there were three, with Gakatiti and Gaka Kume Bless having made an unheralded arrival.They were just there. Gakatiti was a somewhat nebulous individual -- thrown in, apparently, for sheer numbers. He offered little in the way of originality but was willing to go along for the fun. Gaka Kume Bless was the killjoy, or as the mother expressed it, "a kind of God-like creature who acted as a stabilizer." Perhaps Gaka Kume Bless was Michael's conscience, the sensible part of the youngster that kept him from going too far when his more reckless self beckoned.

Certainly each member of the group serves the child in his own particular way. Michael, for example, played card games with Gaka and one can easily guess, when a little guy has been low man on the totem pole with older brothers and sisters, who was invariably the winner. But Gaka served another purpose as well. For, although he was always the loser and frequently became angry and disagreeable, it was through him that Michael learned to lose graciously. Meanwhile, Michael, the gleeful winner, was capable of benevolent generosity toward his opponent.

Another group with similar names was invented by Larry, a 3 1/2-year-old who named his friends Mr. Kungson, Mrs. Kungson, Mrs. Cubes, and Cubeson. This group was different in that they were adults and when Larry spoke of them, he considered himself an adult as well. We also see here the lesser individual in the form of Cubeson. Apparently he was not even worthy of a title, and if perchance, one of the family inadvertantly spoke of him as Mr. Cubeson, they were immediately corrected. "No, Mommy," Larry would say with an amused little laugh, "Not Mr. Cubeson. Just plain Cubeson." Nor was Cubeson a child. He merely lacked the status one requires in order to deserve a title. And as complicated as their names were, they were never confusing to Larry.

Little popular research seems to be available on the imaginary companion, yet the phenomenon is mentioned occasionally by authorities on child behavior, and a few studies are available in various scholarly journals. Even Arnold Gesell and Frances L. Illg in their book, "Infant and Child in the Culture of Today," give the topic only brief mention.

"The imaginary companion," the authors state at one point, "may need a place at the table, he may sleep in or under the child's bed, he may go for a ride in the car. The child is often demanding about the rights of his imaginary companion and very solicitous in teaching him many things."

One interesting comment regarding the use of the imaginary playmate as scapegoat comes from Edith G. Neisser, author of "Primer for Parents of Preschoolers."

"Miss Beibler was the imaginary friend of 4-year-old Alicia," says Neisser. And apparently Miss Beibler was a difficult friend indeed whom her creator had to scold, spank, reprove, and discipline in a number of ways because of her obstreperous behavior.

"Through the wicked Miss Beibler," Neisser tells us, "Alicia was getting rid of, or displacing,' some of the guilt her conscience imposed on her, although she had no idea Miss B. was serving so complicated a purpose. In rebuking Miss B., Alicia was also taming her own tendencies toward wildness."

Our son once had an imaginary "thing" -- a kokonitus. It had dimensions, substance, and personality, and was so fragile no one ever touched it until we moved. Then, with great delicacy and care, my husband packed it securely in an imaginary box under Greg's explicit directions. Perhaps our son just forgot it, or it may have been left on the moving van, but after we got into our new home, we never heard about it again.

Your own child's imaginary playmates could take on any shape, personality, or sex. They might even be in animal form; or perhaps you'll entertain a whole group as we did that memorable summer. Whatever they are -- animal, vegetable, or mineral -- they should offer you no cause for concern.

"Fantasies and dreams!" says Horton. "They are our lodestars."