Although strongly promoted by Southeast Asia's noncommunist nations, a show of unity by three anti-Vietnamese Cambodian resistance leaders mainly benefits one of the groups: the communist Khmer Rouge.

Friday's joint declaration by the three leaders that they would work toward the formation of a coalition government seems likely to put the two noncommunist parties on the defensive in the middle of a propaganda war as they try to justify their action to their own followers.

These are among the worries of Cambodia's former head of state, Prince Norodom Sihanouk, and his onetime prime minister, Son Sann, who both somewhat reluctantly signed the joint statement with Khmer Rouge leader Khieu Samphan.

Outweighing the misgivings of Sihanouk and Son Sann are their hopes that the common stand against the Vietnamese occupation of Cambodia will bring their groups foreign military and financial aid, notably from the United States.

In an interview Sunday, Son Sann renewed an appeal for American aid. He said his Khmer People's National Liberation Front needs arms and ammunition to equip an additional 30,000 soldiers. His party already claims to have 9,000 fighters in settlements along the Thai-Cambodian border, plus 10,000 "guerrillas" scattered throughout Cambodia.

Son Sann said his forces currently are short of food and weapons and are having great difficulty getting ammunition to fighters in the interior. He said his front also needs weapons such as antitank guns, mortars, mines and recoilless rifles to carry on their part of the guerrilla war against the Vietnamese occupation troops.

The 70-year-old former premier indicated that although his front has received military aid from China, obtaining supplies from the United States now is more important than ever because of a need to counter a possible adverse reaction in Cambodia to the signing of an agreement with the Khmer Rouge.

The Cambodian Communists receive a steady flow of military and other aid from China.

Son Sann said he expected the Vietnamese to mount a propaganda campaign to discredit his group by charging complicity with the Khmer Rouge. At the same time, he said, the Khmer Rouge could be expected to tell Cambodians that the joint declaration proves their claim to have abandoned their harsh policies and renounced communism.

"It's a very hard sacrifice," Son Sann said of the joint statement. He added that his group would now try to explain the agreement to Cambodians inside the country, an effort he said would be slow and difficult.

However, he said, "if the United States helps us, the people in the interior will believe us."

"The Khmer Rouge are the winners in Singapore," Son Sann said. "They are not going to execute the agreement. They already got what they wanted."

What they wanted, participants in the talks here said, was a show of unity with Sihanouk and Son Sann that would improve the Khmer Rouge's abysmal image and ensure a decisive victory in a vote on its U.N. seat later this month.

Although driven from power in January 1979 by Vietnamese invasion troops and discredited by the brutality of its rule, the Khmer Rouge government, known as Democratic Kampuchea, retains U.N. recognition as the legal government of Cambodia. Noncommunist countries in Southeast Asia, as well as China and the United States, want to maintain this recognition to deny the Vietnamese a fait accompli in Cambodia.

Friday's agreement calling for a "coalition government of Democratic Kampuchea" to work for "the liberation of Cambodia" serves the Khmer Rouge's interests. But the Communists have little to gain and much to lose by actually joining a coalition on terms set by Son Sann.

Son Sann has demanded leadership of the coalition and a majority of its posts for his group, plus the self-exile of Khmer Rouge leaders "compromised" by the excesses of their bloody rule from 1975 to 1979.

The conditions came up in a meeting Sunday between Son Sann and Sihanouk, and the prince said afterward he had asked Son Sann to "soften a little his position." However, Sihanouk indicated he understands Son Sann's concerns. "Nobody trusts the Khmer Rouge," Sihanouk told reporters. "Nobody believes the Khmer Rouge have changed. Son Sann told me that they lie when they say they are no longer Communists."

Sihanouk said that the first meeting of an ad hoc committee to negotiate a coalition government would be held in Bangkok at a date to be determined. But given the continuing distrust and differences among the parties, it would appear unlikely that the committee could produce a coalition.

Even so, merely having signed Friday's joint statement could discredit Sihanouk and Son Sann among their followers in Cambodia, where the Khmer Rouge are blamed for the deaths of 1 million to 3 million people.

"Inside Cambodia, there is very little chance of it being accepted," Sihanouk told a news conference yesterday with his customary candor. "People won't be enthusiastic." He admitted that he also was unenthusiastic about the agreement.

"My people may condemn me for joining the Khmer Rouge," he said. "To cooperate with the Khmer Rouge is to cooperate with the killers of the people of Cambodia."

As a result of the agreement, however, Sihanouk said he was sure that eventually "the government of the United States -- perhaps secretly, not openly -- will help me to form a big nationalist army to do harm to the Vietnamese and the Soviet Union and make them accept Cambodia as a buffer zone" between Southeast Asia's communist and noncommunist countries.

For good measure, the prince heaped praise on President Ronald Reagan, even recalling that he was one of Reagan's "warmest fans" when he was still an actor and Sihanouk a student in Saigon.

"Not only was he a loved actor, but he is a great statesman," Sihanouk said. "Ronald Reagan is the man we need at present to lead mankind to freedom."