DHAHRAN, SAUDI ARABIA, SEPT. 12 -- The first rumblings of Saudi discontent with the behavior of American troops have begun to surface in complaints being heard at courts of the royal ruling family and in colorful, but apparently fictitious, tales of misconduct making the rounds here and in Riyadh, the Saudi capital.

Several Saudis who have recently gone to the daily majlis, or public council, of the vice governor of the Eastern Province, Prince Fahd bin Salman, asked why American soldiers were carrying their weapons while at shopping centers and why female U.S. soldiers were being allowed to drive cars while Saudi women are forbidden to do so.

Stories about alleged misbehavior by American female soldiers also are circulating, although there appears to be no factual basis for any of them. According to one such account, a female soldier was driving a military jeep near here when she was stopped by an enraged mutawa, an Islamic religious policeman, who demanded she get out.

The soldier obliged, the story goes, but then she went up to the mutawa and delivered him a karate chop that sent him flying.

Another version on this same theme circulating in Riyadh has it that a female American soldier driving a military car was stopped by a mutawa at a red light. The mutawa was then joined by a traffic policeman whom the female soldier shot when he ordered her to get out of the car.

It is not clear who is behind these fictitious stories but some mutawain have made it clear to Western reporters that they are not happy with the large American military presence in a country where two of Islam's most sacred religious sites are located -- at Mecca and Medina.

The mutawain are under the Committee for the Encouragement of Virtue and the Discouragement of Vice and act as "enforcers" of Saudi Arabia's puritanical form of Islam known as Wahhabism. They are easy to identify by their long beards, brown robes and aggressive religious behavior and often carry batons to prod storekeepers into closing their shops for the five daily prayers prescribed by Islam.

Several black-bearded, English-speaking mutawain showed up at the joint U.S. military-Saudi government press center at the Dhahran International Hotel two weeks ago and tried to set up their own bureau to monitor the behavior of Western reporters. They also apparently hoped to proselytize because they came with piles of literature on Islam and Christianity.

One was seen taking notes furiously while he watched a show on CNN television, which is being relayed into the press center through the Armed Forces Network. A love scene apparently was upsetting him.

Local authorities and the Information Ministry finally prevailed upon these mutawain not to set up an office and to forgo trying to convert Western reporters here to cover the U.S. buildup.

Since the arrival of the first American troops in mid-August, the mutawain have kept a relatively low profile, although a few female reporters have had confrontations of one kind or another. According to one report, local authorities have asked for the indulgence of the mutawain in the face of a grave national crisis that has required the kingdom to call in non-Moslem military forces.

U.S. Embassy and military officials say they have received few complaints from the Saudi government about misconduct by any American troops and Saudi officials seem anxious to play down reports of any complaints or friction with the Saudi public.

Gen. H. Norman Schwarzkopf, chief of the U.S. Central Command and the top American military officer here, said local American commanders have been designated to handle complaints from Saudi citizens in a system similar to that established in West Germany to improve relations there with the host country.

"Saudi Arabia has deliberately been kept isolated from the Western world," Schwarzkopf said. "Now a major part of the Western world has been thrust directly in the middle of their sovereignty. That is going to cause some problems. . . . We're doing our best to be culturally sensitive."

Capt. Michael Sherman, director of the Joint Information Bureau, said the U.S. military command has on numerous occasions repeated standing orders that soldiers who go shopping or downtown while off duty should, whenever possible, go without weapons and in civilian dress.

But he said there were "obviously" occasions when soldiers were stopping by grocery stores and shopping centers to buy cold drinks or food while they were in uniform and armed.

"We're here as guests. We have to be aware of the host country's sensitivities. If it's bothering some people we'll try to accommodate them. But I think we've maintained a rather low profile," he said.

Sherman said another problem is that most American soldiers have come here without civilian clothes.

From the start of Operation Desert Shield, U.S. commanders realized there was likely to be a problem of American soldiers adapting to the ultra-conservative customs of Saudi Arabia -- where there are no bars, movies, discotheques or dancing and women are hidden behind black veils.

Generally speaking, few American soldiers have had much contact yet with the Saudi public. Most have been confined to their bases or sent to desert posts far from the main cities and towns.

But Sherman said these orders are slowly changing as enough soldiers arrive to begin instituting shifts allowing free time for some to go into town.

How American soldiers and Saudis will cope with each other if these groups become larger remains to be seen. But U.S. commanders are talking about providing recreational facilities in isolated seaside settings in Saudi Arabia or in places outside the kingdom, hoping this will help to avoid social friction between their troops and Saudi civilians.