It was a typical enough scene: a group of mothers trying to conduct a club meeting while their children ran freely about the room, delightedly disrupting the proceedings. What made it a riveting sight, though, was that nearly every child in the room had a double: a twin brother or sister.

This was the monthly meeting of the D.C. Mothers of Twins Club, a 50-member organization started last spring for families of twins in the District.

The club was started by Carolyn Carter, who for years had to decline invitations by mothers of twins clubs in Maryland and Virginia because she was too busy raising her two sets of twins.

Carter said she and her husband, James, thought their family was complete when she had her fourth child at the age of 23. Seven years later, she learned she was pregnant with twin boys. Eleven months after Wendell and Wayne arrived, she delivered twin girls. "It really wasn't planned," she hastened to add.

Now that all four of the twins are in college, Carter said, she finally has time to catch up on the activities she missed while busy caring for four babies.

"I always wanted to do something to help others," said Carter. When her children were small, she said, she often told the other clubs, "I really can't get to the front door right now."

The District organization is open to fathers as well as mothers. Its goal is to provide moral and material support to families of twins.

"A couple weeks ago a mother called and wanted to know why she was so depressed since the twins had been born," Carter said. "I talked to her about my experiences and she said she felt much better when we finished talking."

The group sponsors clothing exchanges and sales and is planning to establish a scholarship fund for twins. Members also hope to set up a hot line that new or expectant parents of twins could call for information or in a crisis.

"One of the reasons that the work we do is very important is because a girl finds out she's going to have twins and goes to the library to find some books on twins and all she gets is some kind of psychological research," said Marion Meyer, executive secretary of the National Organization of Mothers of Twins Clubs Inc. (NOMOTC), of which the D.C. club is an affiliate.

"We want to educate the public to the fact that twins are ordinary human beings who just happen to share the same birthday," she said.

Carter's daughter Stephanie, 19, however, maintains that she and twin sister Stacey sometimes shared thoughts as well as birthdays when they were growing up.

"If we went out to buy a card for my mother, I would get the same card she had gotten even though we weren't together," remembered Stephanie. "We'll say the same thing at the same time. And we enjoyed dressing alike until eleventh grade. After we got older we decided it was kind of stupid."

Donald M. Keith, executive director of the Center for the Study of Multiple Birth, believes there is a special bond between twins. "This bond," said Keith, who is an identical twin himself, "is often stronger than the bond between mother and child. It ranges from, at the one end, nothing, to . . . sharing pain."

When Keith fielded questions at a recent meeting of the D.C. Mothers of Twins Club he emphasized the importance of parents' helping their twins develop separate identities.

"I told them that they should start with mini-separations," he said in a telephone interview. "One goes to McDonald's with daddy and one goes to Burger Chef with mommy and then they share the little toy that each of them got. They learn that they can have successful experiences on their own."

It is equally important, Keith emphasized, for parents of twins to make sure their other children get adequate attention. "You just have to call everybody's attention to the other children and build them up in everybody's eyes," he said.

Keith estimated that about 7,000 twins live in the District, based on statistics showing that twins are about 1.17 percent of the world's population. That estimate may be low, however, because blacks, who form about 70 percent of the city's population, have a higher than usual rate of twin births: black women have twins approximately once in 79 births, compared with one in 87 births in the general population.

Identical twins, about a third of the twin population, are produced when a single fertilized egg splits in two shortly after conception. They have the same blood type, hair and eye color and the same nose, ear and lip shapes and are always the same sex. Identical twins will not necessarily look exactly alike. They can be positively identified as identical only through blood samples and fingerprints.

Fraternal, or nonidentical, twins are formed when two eggs are released simultaneously from the ovaries and are fertilized by two sperm. They may be different sexes and are not necessarily any more alike than any two children born to the same parents.

The reason twins are born is unknown. But Keith said that a professor from Nigeria--where the incidence of fraternal twins is a remarkable one in 22 births--has been advancing the theory that the phenomenon is related to diet.

"He has pinpointed yams a Nigerian staple as a possible cause," said Keith.

Whatever the reason for their birth, raising twins is an undisputed challenge. Carolyn Carter returned to work nine months after her twin boys were born. But when the girls came along, she couldn't find anyone who would keep four babies, so she had to stop working, she said.

"I never slept," she said. "I had to get up for a six o'clock feeding for all four. Then they had to be bathed and have their hair combed. Then it was time for a 9:30 feeding, and in between I had to start on the housework. I never did get to watch soap operas or go anywhere."

But despite the extra work they require, Georgia Booker, mother of 2-year-old twin boys, Brandon and Brian, and a 4-year-old girl, said she feels that having twins is special. "They're a real blessing. It's the best thing that's ever happened to me. Her husband, Sylvester, said he feels "honored" to be the father of twins.

Nancy Kahane, a nurse, also was excited when she learned she was carrying twins. "I was profoundly shocked," she recalled.

The real shock, according to Kahane, came after she delivered and had to learn to care for two breast-feeding babies at one time. Her husband, Will, who is working at home temporarily so he can help care for 6-week-old Benjamin and Ariel, usually distracts one twin while Nancy nurses the other, a technique that is not always successful.

"As soon as they're both asleep, we both just fall down wherever we are and try to get some rest," Kahane said.

The exhaustion can lead to depression for some parents, especially mothers, twins authority Keith said. The experts bear him out: Carolyn Carter said she "stayed sort of depressed, and the work load was overwhelming," and Nancy Kahane is "worried about what I'm going to do when I have to be alone."

The NOMOTC newsletter advises arranging for outside help or eliminating as many household chores as possible. "The house will wait--your family will not," advises the publication, "Your Twins and You."

Most twins are born prematurely, unlike the Kahanes' boys, born at full term and weighing 7 1/2 pounds each--two pounds above the average twin weight. The low birth weight of premature twins often results in respiratory and other health problems. The mother is also at greater risk during delivery because complications are likely.

At a recent meeting, Thomas Meyer, who helps his wife, Marion, in the national twins organization, introduced himself by saying, "We've got 27-year-old twins . . . --just to give you hope that they do grow up."