The arms race with the Soviet Union is starting to intensify. Also the legs race, the eyes race, the trigger-finger race and the percentage-of-body fat race, as well as the race by certain chauvinists to build better athletes through chemistry -- and the equally spirited race by concerned officials to keep that from happening.

Sure looks like a little good news this past week: U.S. and Soviet sportsmen signed an agreement that, if their politicians cooperate, assures that the 1988 Seoul Games will be the closest to a genuine Olympics in history.

A mouthful called "Accord of Mutual Understanding and Cooperation in Sports" means that Soviet kids and ours can play together in the world's sandbox again.

Athletes from both countries have been doing that, now and then, during and after boycotts, we of their Moscow Games in '80 and they of our Los Angeles Games last year.

Still, assuming the best, the '88 Games will be the first time in 12 years that the Soviet Union has experienced the overhauled United States Olympic machine with the pedal to the (gold) medal.

It's sleek and swift.

Soviet leaders got their initial up-close look at the surge in U.S. amateur sport during a tour of facilities in Colorado Springs after the accord was signed in Indianapolis.

They reportedly were astonished at sights that included American athletes training full-time in such obscure sports as shooting and women's volleyball.

Soviet-bloc domination of the Olympics has been largely through disciplines in which U.S. athletes have shown little or no enthusiasm.

The Soviets and East Germans do not discriminate among sports, subsidizing biathletes and team handball players as heavily as sprinters and power forwards. To their comrades in the less-glamorous Olympic events, Marat Gramov, president of the Soviet Olympic Committee, may be yelling:

"The Americans are coming; the Americans are coming."

Exhibit A was a women's volleyball match last week in Colorado Springs: the U.S. vs. Italy. An estimated 2,000 people paid $7 each to watch. That sort of interest in women's volleyball is a spectacular contrast to the times, not long ago, when a tour by a Chinese team could not generate crowds of more than a few hundred, although admittedly there is likely to be great interest in anything Olympic in Colorado Springs, home of the Olympic training center.

America's sweetheart, Mary Lou Retton, probably earned $300,000 or so last year. The other gold medalist from West Virginia, rifle shooter Ed Etzel, got spoils that included a four-wheel-drive vehicle.

Perhaps a dozen American skiers and track and field athletes are millionaires, or at least in their trust funds, to which endorsements and other income must go and from which training and living expenses flow.

It's an innovation, all perfectly legal, from the last time the Americans and Soviets collided in the Olympics. In those '76 Games, corporate sponsorship in U.S. sport was mostly a dream. It's now a megabucks reality.

Ten years ago, Frank Shorter testified before the President's Commission on Olympic Sports about how he and other American athletes were forced to scratch, sometimes through under-the-table payments by promoters, to exist.

Through trust funds, everything is inching above board, to the point where bright and dedicated American athletes can earn both money and practice time from enlightened companies.

When the best hurdler of his time, Renaldo (Skeets) Nehemiah, joined the San Francisco 49ers four years ago, he needed a staggering contract to avoid taking a pay cut to relinquish his amateur standing.

The vast majority of U.S. Olympic athletes still makes no more than the vast majority of Americans. Which also is fine, the government having no business getting involved in mass-producing javelin throwers and synchronized-swimmers.

According to the former executive director of the President's Commission, Mike Harrigan, the U.S. Olympic Committee raised about $12 million between '72 and '76, about $55 million between '76 and '80 and about $90 million between '80 and '84.

That's about $90 million and counting, for not all the pennies from the Los Angeles binge have been distributed. In the end, it is whispered that each of the 38 U.S. governing bodies might receive $1.3 million.

That's a mighty windfall for, say, men's field hockey. All along, the President's Commission insisted that if American amateur sport ever got its act together good things would follow.

It has, and they have.

The surge in U.S. funding for amateur sport hit the Soviets in the '80 Winter Games. The major reason for the ice hockey upset -- and subsequent gold medal -- was the U.S. players being able to spend a significant time together.

Part of the accord is an exchange of coaches, athletes, officials and training-camp visits. I long have held that Soviet basketball would improve dramatically if several dozen promising players could be dropped off in Washington-area playgrounds each summer.

"I think the Soviet athletes are on kind of a down," said the executive director of the U.S. Gymnastics Federation, Mike Jacki, "same as our athletes were on a down after the '80 boycott.

"The Soviets are more agreeable now, partly, to lift the morale of their athletes -- and to see what they're going to be up against for the '88 Games."

For the first time, if most of us are at peace, the global philosophical struggle will spill over into sport:

Communism vs. capitalism.

Anheuser-Busch vs. the Red Army.