When Americans visit Ho Chi Minh City, the children invariably seek them out. They gather around displaying letters, identity papers and sometimes photographs of their American fathers who left them behind in Vietnam.

They are among the tens of thousands of Amerasian children scattered in several countries across the Far East. In Vietnam especially, they stand out as living reminders of an ill-fated U.S. military involvement. Many are beggars or urchins who eke out a living as peddlers on the streets of the former South Vietnamese capital. And many desperately want to join their fathers in the United States.

Because of regulations in both Washington and Hanoi, only 23 Amerasian children have left Vietnam since 1980 under an Orderly Departure Program for legal emigration. Now, however, the gates seem to be opening wider, with signs of a new attitude toward the problem by both sides.

Indicative of this, 11 Amerasian children and nine accompanying relatives are scheduled to leave Vietnam Thursday for Bangkok on their way to the United States.

According to Donald Colin, Bangkok-based director of the Orderly Departure Program, the seven girls and four boys ranging in age from seven to 15, will be the largest group of Amerasian children to leave Vietnam so far. He said at a news conference today that 10 of them are to be reunited with their American fathers. The father of one has died.

One of the parents is making the trip personally to Ho Chi Minh City, formerly Saigon, along with U.S. consular officials, representatives of voluntary organizations and journalists. Gary Tanous, a former civilian employe in Vietnam from Vancouver, Wash., has been battling for the past three years to get permission for his daugther Jean-Marie, 15, to join him in the United States.

Tanous began his struggle with the Vietnamese and U.S. bureaucracies -- he has been critical of both -- when he learned that his Vietnamese ex-wife had abandoned their daughter and fled Saigon at the time of the Communist takeover in 1975.

"To say I am ecstatic is an understatement," Tanous told reporters after learning his daughter would be among the 11 children. He added: "I have to be grateful to Vietnam for this."

Asked why he thought Vietnamese authorities now were allowing the 11 children to leave, Colin said, "I suspect they hope they will get some good publicity out of this, and they probably deserve it."

"This is the time of year when they try to do good things because of the U.N. General Assembly," he added, referring to a dispute over the seating of Cambodia, whose Vietnamese-installed government has been seeking U.N. recognition in place of the ousted Khmer Rouge regime.

In any case, the departure of the 11 will barely make a dent in the Amerasian problem in Vietnam, officials here said. According to Colin, his office now has files on nearly 4,000 Amerasian children in Vietnam "who have a burning desire to leave the country now." In addition, he said he receives a couple of hundred letters on Amerasians a week, about 75 percent of them on new cases.

If the departure of the 11 generates enough publicity, Colin estimated his office could get immigration requests from 4,000 more Amerasians in Vietnam. He said there were probably about 8,000 Amerasian children in Vietnam who have not been assimilated into society and want to leave. Other estimates have put the figure much higher.

Vietnamese authorities have spoken of 8,000 Amerasians in Ho Chi Minh City alone. And some unofficial sources have estimated there are about 30,000 in the rest of southern Vietnam, where more than 2.5 million American soldiers served and hundreds of thousands of U.S. civilians worked during the Vietnam War.

John Shade, director of the Pearl S. Buck Foundation, has estimated that there may be as many as 250,000 Amerasian children in Asia.

Thousands of Amerasians were left in Korea, Japan, Thailand and the Philippines. Many of them, especially the children of black Americans, suffer from prejudice, and many grow up in homeless poverty. Some resort to prostitution to make a living.

Amerasian children are particularly subject to social ostracism in Vietnam, where they are often identified with Hanoi's former enemy.

In what some critics see as a belated effort to face up to American responsibilities on the issue, Congress is currently considering legislation that would allow more Amerasian children into the United States by improving the visa eligibility of those from Vietnam, Korea, Thailand and Laos.

In a bid to put the ball in America's court, Vietnamese Foreign Minister Nguyen Co Thach has said Hanoi would let all the Amerasian children leave if the U.S. Congress passed the necessary legislation.

Colin said that meanwhile the Vietnamese have agreed to make greater efforts to locate persons who have U.S. citizenship or are eligible for it. He said that to be classified as an Amerasian, a child needed to have evidence, including "something to identify the name of the American father and who he was associated with in Vietnam."

Currently, the U.S. Embassy in Bangkok has a list of 88 Amerasian children classified as U.S. citizens, including the 11 scheduled to leave Thursday. At present, this is the only category of Amerasians eligible for inclusion in the Orderly Departure Program.

So far, Colin said, 6,631 people have left Vietnam for the United States under the program since it began in 1979, a fraction of those who want to leave. In addition, Colin said, his office has 96,000 files representing nearly 470,000 Vietnamese who want to go to the United States.