For 12 American families the ordeal of Vietnam ended yesterday. They had been separated - husband from wife, parents from children - for more than three years, ever since the collapse of the Saigon regime trapped some of them inside communist Vietnam.

As David Gerzevske of Oak Park, Ill., wept and embraced the son he had never seen, as Elizabeth Page of Baltimore hugged a Vietnamese born grand-daughter she would only now begin to know, and as a score of other people made their way from Dulles Airport to flights that would take them to cities all over the United States - and the loved ones who live there - they were also marking what many believe is a new and happier stage in relations between the United States and Vietnam.

"I'm just thankful that this day ever came," said David Gustavsen of Swampscott, Mass., whose Vietnamese wife and daughter and, unexpectedly, a niece as well, had arrived after a 27-hour flight from Bangkok, Thailand.

"I don't think any words could be added to the happiness and emotion," Sen. Edward Kennedy (D-Mass.), said at the airport after the jet arrived. Kennedy had been instrumental in securing the release of these families. "I think their embrace means more than any words from any of us."

For three years the International Red Cross, the United Nations High COmmissioner on Refugees, the U.S. State Department and numerous other voluntary agencies had worked for this day.

"We lived and breathed this," said Dorothy Taaffe of the American Red Cross. "Fathers had to be found, the families contacted, and again and again we talked with the Vietnamese without getting anywhere."

At every diplomatic meeting between Washington and Hanoi, including the last Paris talks in December, Hanoi insisted that the question of Vietnamese-born wives and children of American citizens was simply a consular issue that could be taken up after other major questions of diplomatic relations - such as the problem of once-promised reparations payments - were dealt with.

After those last Paris talks, and then the unprecedented explusion of Vietnam's ambassador to the United Nations on charges of spying, relations between the two countries appeared to be at a new low.

"We started when things were in the doldrums," said Jerry Tinker, a Senate Judiciary Committee staffer who works closely with Kennedy on humanitarian issues, and who accompanied the American delegation that brought the families out.

Through the winter and early spring Kennedy's people used lines of communication that have been open to them since the time of the war to express their concern for the familes.

"When things break down," said Tinker, "we can maybe still make progress on certain specific issues."

At a meeting the mid-May, Kennedy's people told the Vietnamese that they understood the problem was a consular one, but that it had been going on so long it had become a humanitarian concern as well, Tinker said yesterday.

Representatives from Kennedy's office presented the Vietnamese with a list of 15 children inside Vietnam who were American citizens with American passports, and suggested their release would be a first step to solving the problem.

"They bit on it so fast," said Tinker, "it almost took us by surprise."

By june 21 a formal announcement of the release of 29 people was made, and since then the only problem has been arranging details for the transportation of the children and their Vietnamese-born mothers.

"This is a very positive and hopeful sign," Kennedy said yesterday.

Archbishop Philip M. Hannan of New Orleans, who led the delegation to Vietnam, said the Vietnamese had made it clear to him that the release of these children with passports is only the first step.

"They have given us a flat assurance that they will continue to process others who are separated from their families, he said.

The mission, Hannan said, "was extremely successful, not only for now but for the future."

It is, indeed, the first real hope that has been held out to approximately 300 Americans with close relatives trapped in Vietnam since the end of the war, the first chance for hope that thousands of Vietnamese living in the United States have been given for the reunion of their war-torn families.

But yesterday, at the weary travelers shielded their eyes from the glare of countless television lights their minds were mainly on getting home.

"Now," said Kennedy as the press conference ended, "we'll just help everyone to just have a quiet time."