The United States has been deploying an average of one Pershing II nuclear missile a week in West Germany since March, according to secret testimony given Congress earlier this year.

Although the controversial American missiles appear to be going into Europe faster and with less public protest than expected, they are creating new problems for the American troops that must handle them and the West Germans who live near their bases.

The first complete Pershing II battalion of four firing batteries with 36 missiles is now at Swaebisch Gmuend in south-central West Germany, according to sources. Nine more missiles for a second battalion have arrived at Heilbron not far to the north, sources said. That means at least 45 of the planned 108 controversial missiles already are in place.

Brig. Gen. James C. Cercy, deputy director of weapons systems for the Army's office of research and development, told a closed session of the House Appropriations subcommittee on defense in March that two batteries of nine missiles each had been deployed as of Feb. 29, and the plan was "to continue the fielding effort at the rate of one battery every nine weeks." The transcript of the hearing was released last month.

The deployment is faster than earlier expected, according to a former Defense Department official who was involved in the original planning in the Carter administration.

Meanwhile, West German and American officials refused to confirm the deployment figures publicly. "We don't want to reopen the public debate," one Bonn official said recently, "particularly with the antimissile demonstrators here a thing of the past."

In part, protests have died down because the Soviets, too, have been adding to their nuclear forces, putting missiles into East Germany and Czechoslovakia and continuing deployments of new SS20 missiles in the Soviet Union at the rate of one a week, according to Pentagon officials.

Because the Pershing IIs' 1,000-mile range, twice that of the Pershing 1a it replaces, enables them to hit targets in western Russia within 14 minutes of launch, they have become a prime Soviet target in the event of war. Moscow has even developed a special commando force whose role at the start of hostilities would be to destroy American nuclear weapons in Europe before they could be used, a senior Pentagon official said recently.

To keep the Soviets guessing where the Pershing IIs are, unarmed missiles are being moved about the countryside with greater frequency than older missiles so troops can gain familiarity with remote sites that would be used in a crisis. And because it is important to keep operations secret, both from the Soviets and possible antinuclear activists, the Pershing II movements, with their convoys, are scheduled for late night or early morning.

It is hard for a traveler through that part of Germany to miss seeing at least one convoy.

Under operational plans outlined in an "information brochure" given to soldiers assigned to the Pershing battalion at Swaebisch Gmuend and obtained by The Washington Post, each of the four batteries in the battalion goes through a 12-week operational cycle.

Only one is on "combat alert status" with a nuclear warhead on its nine missiles. The other three batteries, without nuclear warheads on their missiles, are either in field training, undergoing maintenance or working to put their missiles in shape while on a pre-alert status.

The nine-missile battery from Swaebisch Gmuend on combat alert is located at a guarded facility 100 miles south of its home base, according to the brochure. There, the brochure says, "Your battery's missiles will be kept in a firing position 24 hours a day."

A second battery of nine missiles, on training, regularly carries on field maneuvers during another 12-week cycle. It also serves as a backup alert unit for the NATO commander.

Troops are warned in the brochure that there occasionally are practice exercises when all 27 Pershing IIs not on 24-hour-alert can be ordered to dispersed sites.

On Sept. 24, a Pershing II missile on its launcher was damaged when the roadside collapsed and the vehicle slid down and smacked against a row of trees. That Pershing II unit was on "deployment training," according to Capt. Michael Griffon, the public information officer at Swaebisch Gmuend.

As Griffon described it during a recent interview, the Pershing II transporter carrying an unarmed missile stopped during the night on a gravel spur off a road in a forest about 10 miles from its base.

Though Griffon would not say so, the site appeared a good hiding spot for the missile. At 6 a.m., Griffon said, the "ground gave way and the launcher with the missile slid off the road on its side . . . . There were no injuries and no evidence of equipment failure, but both the missile body and the transporter were damaged."

It took six hours for U.S. Army officials to decide how to pull the 82,000-pound missile and launcher back onto the road, Griffon said.

Meanwhile, the area was cordoned off. At 8 that night, two hours after the missile had been removed, American troops were still cleaning up and a small crowd of onlookers and West German police was milling around.

It was the first accident with a Pershing II, but, given the pace and nature of deployment, officials fear there will be more.