The father wept openly as his sons embraced him for the first time since the fall of Saigon. Wives collapsed into their husbands' arms, little children scampered about their grandmother's feet and greeted with shy smiles the parents they had not seen for as long - well, for as long as many of them could remember.

"It has been three years and two months," said one of their fathers. "You count every day."

The journey that brought all the children and grandchildren of Tran Quoi and Nguyen Thi Chi together at National Airport yesterday began almost three months ago on a Mekong riverboat. The planning and preparation for it had taken almost a year.

They are one family among thousands now coming to the United States almost daily: the "boat cases" who have fled Vietnam onto the open seas with little but the hope that they could some day find a new life and freedom outside their home country.

Chi, the 53-year-old matriarch of the family who handled the delicate and sometimes dangerous arrangements for the escape, walked down the sterile corridors of National Airport yesterday without the slighest sign of misgiving at the prospect of resettlement and adjustment to a new nation and culture.

"In Vietnam," said Chi as one of her sons translated, "we led a life with no tomorrow."

"If you live with the communists," her husband added with sudden vehemence, "you only work for them they said, but then, inexplicably, it until you die. They kill you slowly not directly."

The story they and their children told of their escape was in many ways typical of the boat cases.

Two of their sons and a son-in-law had fled Vietnam in an American helicopter during the last hours of the Saigon regime, and have since been living and working in Rockville. In the violent confusion of the evacuation they could take no more than a few members of their families with them, they said yesterday.

But because two of them had worked at the American Consulate in Chau Doc province their families there soon found themselves the object of recurrent interrogations and harassment.

Another son-in-law, formerly a captain in the South Vietnamese Navy, was sent away to a "reeducation camp" in the North. He has never returned.

The family had owned a restaurant, but soon after the new regime came to power it was closed. With no regular means of support they earned money by turning their yard into a garden and selling food.

To raise money for the escape they slowly sold off virtually all their belongings, and by last spring they had accumulated the 30 ounces of gold needed to obtain a boat.

Chau Doc province is near the Cambodian border, and mortar shells had begun to land regularly not far from their homes. As a result they were able to obtain internal travel documents, they said, that would have been difficult to acquire elsewhere in the country.

By April all the preparations were complete, and with the riverboat's mechanic acting as their captain they set sail downstream - 31 people on a cabinless boat scarcely 40 feet long and less than 10 feet wide.

On the night of April 9 they headed out onto the open ocean in a boat designed for placid river waters. They had no charts or maps. Their only navigation device was an old Army compass which had cost them 1 million piasters - roughly $1,000. For a few desperate minutes they were pursued by a government patrol boat, turned away from them.

After two days and nights they arrived at the coast of Thailand but were refused permission to land. They continued on to Malaysia, then only a few miles away, and there again they met with hostility as people on the shore fired guns over their heads.

"Don't worry," the little children were told. "They won't shoot us. Just keep crying." Finally, they were allowed to swim ashore, leaving most of their belongings on the boat.

"It's a world of luck that we were able to make it out," said Tran Quoi. "It was with the help of god that the sea was so calm."

Ruth McLean of the Lutheran Immigration and Refugee Service, which has taken the responsibility for resettling many of the boat cases coming to this country, told a reporter that the number of Vietnamese refugees who perish on the sea fleeing their homeland is unknown, "but we believe that between 50 and 60 percent never make it."

Last month 217 people reportedly drowned when their boat capsized in the South China Sea. There have been many other reports that the often sinking, leaky crafts have been ignored by passing freighters whose captains feared endless bureaucratic complications if they arrived in port with a cargo of refugees.

By the end of last month the situation had become desperate as the countries within reach of the refugees' boats reportedly refused to let them land, fearing that they would stay.

For the past several months, however, according to Shepard Lowman, director of the State Department's office of refugee affairs, the United States has made it clear to these governments that we will try to accept many of the refugees if they can find nowhere else to go.

Many cannot. At present, according to Lowman, there are about 20,000 refugees like the Trans waiting in Southeast Asia for resettlement. Between 5,000 and 6,000 more are coming out of Vietnam every month.