Still struggling to establish its claim to power, the Vietnamese-installed government in Cambodia faces a growing list of problems that threaten to slow the country's fragile convalescence from years of war, destruction and famine.

Buoyed by Cambodia's gradual efforts to return to normality, the Phnom Penh government has made some strides in setting up political and social institutions. But efforts to consolidate its authority have been held back by its inability so far to build up an effective army.

In addition, a brain drain is eroding the little expertise available as a steady stream of ministry officials and other educated Cambodians heads for the border with Thailand to defect to the noncommunist opposition or seek a better life abroad.

Aggravating this problem is the apparent reluctance of many Cambodians to participate in the reconstruction program. Instead, they prefer to engage in smalltime capitalism after the destructive rule of the Khmer Rouge from 1975 to 1979, which left hundreds of thousands dead and the economy in ruins.

On top of all this, according to foreign residents with extensive experience in Cambodia, are tenuous security and mounting resistance in some provincial areas, where many villages shift their loyalties when the sun goes down.

By contrast, the capital of Phnom Penh appears much more secure, with urban life steadily reviving. The city's free markets bustle with shoppers, and the streets hum with all kinds of small businesses, from sidewalk cafes and barbers to shops selling used refrigerators and television sets that pick up programs from Vietnam.

The traffic on the capital's tree-lined avenues has also been getting heavier. Cars are still rare, but bicycles, oxcarts and pedicabs now compete with an increasing number of mopeds and motorcycles, many of them new Japanese models smuggled in from Thailand.

Although still a long way from the elegance and animation extolled by travelers before 1975, Phnom Penh can boast of a remarkable recovery in the last 2 1/2 years. The city's population, driven into the countryside by the Khmer Rouge, has risen to between 400,000 and 500,000, according to the latest estimates.

On a Sunday afternoon, thousands of Cambodians can be seen lining up to visit such attractions as the former royal palace or strolling along the Tonle Sap River amid vendors hawking ice cream, balloons and various other items.

In the provinces, the Khmer Rouge communists led by Pol Pot -- ousted by the Vietnamese invasion troops in 1979 -- can still claim some support in poor rural regions, whose inhabitants were not displaced or brutalized nearly so much as residents of urban areas. Also working against the government is the longstanding antagonism between Cambodian peassants and city-dwellers, which the Khmer Rouge exploited so successfully during its rise to power in the early 1970s.

Thus in the classic pattern of guerrilla wars, the government controls some places during the day and the Khmer Rouge has the run of them at night, according to foreign residents with close contacts in Cambodia who have traveled widely through the country in the past year. Besides the western border area in Battambang Province, these sources said, the Khmer Rouge can count on some support in rural parts of Takeo, Kampot, Kompong Chhnang, Siem Reap and Kompong Cham provinces -- zones that are nominally under government control.

However, the sources emphasized that support for the Khmer Rouge in the country as a whole remains minimal. They estimated that the forces led by Pol Pot are backed by perhaps 5 percent of Cambodia's population.

Although most Cambodians would probably prefer an independent noncommunist government and would like to see the Vietnamese occupation troops go home, knowledgeable Western officials here said, the Vietnamese are still considered the best insurance against a resumption of brutal Khmer Rouge rule. The prospect of Pol Pot's return to Phmon Penh still seems to cause terror here.

In fact, the fear that the Khmer Rouge may be on the rise is one of the mtivations now being cited by some Phnom Penh residents who are considering fleeing the country, aid officials said. These Cambodians fear that the U.N. conference on Cambodia last month in New York has given the Khmer Rouge new impetus -- and Western backing -- in its guerrilla war against the 200,000 Vietnamese troops occupying the country.

The greatest cause of Cambodians' dissatisfaction and desire to flee, however, is a perceived trend toward tighter political control and ecnomic restrictions by the communist government in Phnom Penh.

In a congress in May, the ruling People's Revolutionary Party of Kampuchea declared an economic policy of "taking transitional steps toward socialism. . . ." Government officials said this means that the free market -- currently flourishing with a wide variety of goods smuggled from Thailand or pilfered from international aid shipments -- eventually will be closed in favor of state0run shops. A large government-owned market is scheduled to open in Phnom Penh by October, officials said.

"Many people are leaving, especially those with money, because the government doesn't want people to engage in big business," said a co-owner of a small family enterprise here.

Among those who have money in Cambodia are nouveau riche traders who have piled up small fortunes from the sale of smuggled or stolen goods, as well as the pre-1975 well-to-do who managed to bury their gold and jewelry before the evacuation of the cities. In fact, according to residents, Phnom Penh by night resembles a big treasure hunt, as Cambodians defy a curfew to sneak back to their old homes and dig out their caches. Those who hid cash are out of luck since the old currency is worthless.

Besides the private-sector Cambodians, a number of high-ranking officials have fled in recent weeks. Among them, one aid official said, were a department head in the Agriculture Ministry, the chief of the Health Ministry's pharmaceuticals department, a Justice Ministry official and the director of a hospital in the port of Kompong Som.

"The movement is going on, although it's not a huge movement," one Western relief agency director said. "I think it's basically economic rather than political. Having come out of a survival phase, people are starting to consider having a normal life, especially if they are educated."

Another agency director said the departures also indicated "a lack of confidence in the government."

Besides the economic grievances, a source of widespread dissatisfaction appears to be obligatory attendance at the government's "political education courses." Cambodians are routinely summoned to attend the courses, which can last for three months and somewhat resemble Vietnam's reeducation programs.

"It's like going to prison," complained one gloomy Phnom Penh resident about to spend two months in political education at a former boarding school in the capital. "You're only allowed out one day a week. It's really miserable."

In addition to the thousands of Cambodians undergoing such indoctrination, the government holds an unknown number of political variously estimated at between 3,000 and 10,000.

So far the government has refused requests by the International Committee of the Red Cross to inspect Cambodian prisons, which are said to hold many citizens suspected of supporting Prince Norodom Sihanouk, the former head of state, or former premier Son Sann.

One account of prison conditions has come from an escapee, Ung Sophal, who fled to Thailand last year after spending four months in jail for holding a Christmas Party attended by several Western aid workers. He told reporters he was accused of links with Sihanouk and the U.S. Central Intelligence Agency, was interrogated three times a day and was kept in a small cell in which he was chained hand and foot and given meager rations. Ung said he was never tortured but that he had heard the sounds of other prisoners being beaten.

The government indirectly acknowledges that it is holding political prisoners but refuses to disclose how many.

Asked about the underground political activities of Son Sann's supporters in Phnom Penh, Vice Foreign Minister Hor Nam Hong said in an interview, "We have been able to arrest their agents thanks not only to the police and the Army, but also to the people."

A knowledgeable Western relief worker said a number of people have been arrested in Phnom Penh since June, virtually all of them Son Sann supporters. He said he did not know of any political prisoners who were released in the last two years.

In Phnom Penh, Son Sann appears to be the most popular leader of those in exile, although Sihanouk reportedly has a vastly greater following in the countryside. Neither figure is given much chance here of returning to power, however, and any association with the Khmer Rouge would be a kiss of death as far as popular support is concerned, Western aid officials said.

"The people in Phnom Penh would prefer Son Sann, but I don't think he has any chance of coming back," said one middle-class Cambodian with an air of resignation. In the cities, this educated Phnom Penh resident said, Sihanouk still suffers from his association with the Khmer Rouge at the time it came to power in 1975 and forced people to evacuate urban areas. Later Sihanouk was put under house arrest and eventually went into exile.

Despite the traces of dissatisfaction and anxiety that lie under the surface of Phnom penh's return to normality, the government has scored some successes in the political and social fields.

Although widely denounced as a sham, legislative elections in May for a 117-member National Assembly have enabled the government to claim a popular mandate. The National Assembly last month chose a new administration consisting of a Council of State and Council of Ministers, and it adopted a new constitution giving overall dominance to the communist People's Revolutionary Party of Kampuchea.

With the help of international aid, the government also has set up numerous hospitals, orphanages, schools, theaters and other facilities.

All this and the transition from rule by a provisional, Vietnamese-installed People's Revolutionary Council to formal government institutions nominally based on elections has given the government greater self-confidence, according to Western aid officials. It has been shown, they said, in the government's dealings with international aid agencies and the development of closer, more direct ties with the Soviet Union independently of the Vietnamese.

The international organizations involved in the U.N. emergency relief program in Cambodia are the International Committee of the Red Cross, the U.N. Children's Fund, the Office of the U.N. High Commissioner for Refugees, the World Food Program and the Food and Agriculture Organization. In addition, numerous voluntary agencies, many of them church groups, have sent representatives to Phnom Penh.

Apart from India, only the Soviet Union, Vietnam and their East Bloc allies maintain diplomatic missions in the Cambodian capital.

The Cambodian authorities also seem to be taking a bit more credit these days for the fight against the Khmer Rouge.

"We have reason to be proud of our progress," Hor Nam Hong said. "It was our people who rose up with empty hands and, with the help of our Vietnamese friends, overthrew Pol Pot."

He said the Phnom Penh government's Army was "making progress" and engaging the Khmer Rouge in combat. He added, "Our Army is training every day: the soldiers are learning while fighting the rebels."

The Cambodian Army claims to have 30,000 troops, but they reportedly are poorly equipped and trained. Moreover, they do not appear to have the complete trust of their Vietnamese advisers.

No major units are known to operate independently of the Vietnamese, who tightly control the fledgling Cambodian military.

During trips to the town of Kompong Chhnang, about 75 miles north of Phnom Penh, and to the port of Kompon Som, 135 miles southwest of the capital, many of the Cambodian soldiers seen guarding roads and buildings looked to be inexperienced teen-agers. The few who were armed often carried only World War II-vintage carbines, and their positions were vastly outnumbered by those of Vietnamese troops.

Hospitals regularly admit young soldiers who accidentally wound themselves or each other with their guns. In the Kompong Chhnang hospital, for example, one of seven patients recently admitted with bullet wounds was a youthful town militiaman who had shot himself in the leg. Sitting on a bed and wearing a Yamaha T-shirt, he said he was 18 years old, but he looked about 14.

At the Samaki Hotel in Phonm Penh, a visitor recently was startled by the sound of rifle shots just outside the building. But an unperturbed aid official dismissed the incident, explaining that the young Cambodian soldier guarding the entrance had a habit of frightening pesky children away by firing over their heads.

Most Western aid officials, and apparently many Cambodians here, believe that without the Vietnamese troops in the country, the Khmer Rouge would be back in the capital in no time.

Perhaps the best illustration of the state of the Phnom Penh government's Army is the account, possibly apocryphal, of a relief worker who asked a guard for a look at his rifle.

Finding it empty, the relief worker asked the young soldier what was the use of standing guard with an unloaded gun.

"That's okay," the Cambodian replied. "My Vietnamese friend here has the bullets."