"When are we going to learn to kick the other guy?" the children -- with visions of the movie "Karate Kid" -- ask the aikido instructor.

It's a question adults think but don't voice.

"We don't kick anybody or hit anybody," says George Simcox, 51, third-degree black belt and chief instructor of the Virginia Ki Society, the oldest and largest aikido group in the Washington area. "Focus on becoming harmonious with the universe in which you're operating, rather than becoming antagonistic."

That answer is invariably confusing to both children and adults steeped in the more instant gratification of American society. With none of the flashy moves of judo or karate, aikido -- once considered too esoteric for a practical populace -- is quietly coming into its own, recognized more and more by devotees for what they see as an ideal combination of self-defense and relaxation.

Tokyo police were trained in aikido for security measures during President Reagan's trip to Japan. Compared with 300 students 10 years ago, 2,000 students a year -- men, women and children -- now go through the Virginia Ki Society, and about 1,600 participate yearly in Montgomery County Aikido Society sessions.

Even with the "image problem" of aikido -- "It looks a little balletish, which means it looks a little panty-waisty," says Simcox -- it is especially popular among former students of "kill-type" martial arts.

Simcox, who in his other life is a program development officer for the Engineer Topographic Laboratories, is used to the aggressive "busting boards" image of martial arts.

"There are a lot of people who want kill-type instruction. It certainly serves a purpose in a society. But people tend to immediately look at any kind of martial arts group and decide they're all the kill crowd. We're completely the other way."

One 10-year black belt karate student gave up karate and took up aikido when a friend came running up to "buddy-buddy" him and pat him on the back, and his immediate reaction was to throw him down. (He didn't.)

Aikido sessions begin with legs tucked under the hips, Japanese style, in a dojo (school), with the sensei (teacher) in black or navy hakamas (long divided skirts). Students bow to pay respect to aikido and to each other.

Students are taught first to "center," initially practiced by placing the right index finger about 2-3 inches below the navel, at the body's physical center of gravity. Students press hard on the point, remove the finger and try to continue sensing all actions and thoughts springing from this point. The student is relaxed, balanced and grounded, but ready for anything.

Simcox estimates that 45 percent get the idea of centering right away; 30 percent think you're insane and the rest are skeptical. "Strangely enough, the skeptics become the better students."

George Leonard, a student, teacher of aikido and author of The Ultimate Athlete (Avon), tells about an aikido student walking along a city street late at night when two men approached. He heard the sound of a switchblade flick open.

"If I'd had time to think," the student says, "I probably would have freaked. But it was so unexpected that I just centered."

He and the two attackers stood motionless for a few seconds. Then the man with the switchblade relaxed, closed his blade, and said, "I guess we got the wrong guy . . ."

In aikido, the force of the attacker is used to help the defender get out of the way. "We have a saying that 'you meet yourself on the mat.' "

"Aikido is all circular -- you move sideways out of the way of a linear attack," explains Martha Kaufman, 33, a D.C. political fund-raising consultant who took aikido to supplement her black belt in karate.

"In karate you meet force with force rather than force with deflection. In aikido you might end up behind the person who's attacked you. You learn how to move much better with aikido."

While aikido is an effective self-defense method, it is not the focus of the art, especially in ki-aikido, a branch of aikido which concentrates on mental control first.

Simcox, who started with aikido in 1966 in Tokyo, concentrates on what students are "going to do most of the time, which isn't fighting and conflicting with people, but rather trying to get harmonious relationships."

Students learn, for example, how to maintain balance -- instead of becoming irritated -- on the subway when someone bumps them.

For most western minds, the non-competitive, path-of-least-resistance philosophy looks simple but proves difficult.

Writer Leonard, dragged in by a friend in 1970, says he "was often impatient with the hours spent in the nonphysical exercise -- calming and centering my body, sensing the approach of others, blending with putative 'energy flows,' meditating.

"My head could understand all this well enough . . . however, I had learned to delight in competition and aggressive physical action."

It was some time before he learned "that aikido's basic teachings erase those barriers the western mind has erected between the physical and the mental, between action and contemplation."

"I think some women come to develop the more aggressive side, and men come to develop the more feminine side," says Montgomery County student Rebecca Nisley, 34, an editor with the Forest Service. The discipline, she says, has given her more confidence and calm, without competition. "We have a saying that 'you meet yourself on the mat.' "

For children, say instructors, aikido works best with certain ages.

"Six-year-olds will take the idea pretty well. Then about 8-10, they all want to smash each other," says Simcox, "and about junior high they get serious again."

Once convinced, aikido students are eager to talk about how the Japanese philosophy applies to real life.

A house painter, for example, credits aikido for his survival of a fall from a roof. "I kept saying, 'relax, relax.' The doctor says I was pretty lucky."

Lenny Stearns, 29, a systems analyst with MCI and first-degree black belt who started aikido six years ago, says it helps him through job interviews.

"You first have a calmness and then you have an ability to extend your energy out to the interviewer, so it's not as if the interviewer is completely controlling the situation."

"Because we talk of mind and body harmony," says Nisley, "you become much more conscious, when you look at people, of how disharmonious their minds and bodies are. When you see people slumped over on the subway, that says something about their inner selves."

But nevertheless, most aikido students find the mystery of the ancient Japanese discipline -- with its seemingly contradictory combination of harmony and aggression -- difficult to explain.

"You're attacked very firmly and you're thrown, but it's together," says Leonard. "You just have to see it. You see people dashing in to strike somebody, letting go with this tremendous blow and getting thrown and landing 15 feet away, and the whole thing is very loving.

"It sounds kind of crazy, but it really works."

Among D.C.-area aikido schools (prices range from $25 to $45 a month): D.C. Aikikai, Takoma Park, (301) 829-4202; Virginia Ki Society, Tysons Corner, (703) 556-9753; Montgomery County Ki-Aikido Society, Rockville, (301) 774-3477; Capital Aikikai, Georgetown Day School, (202) 229-2330.