Do Thi My was barely 22 when she met an American Air Force major while working at an officers' club at Phu Loi, South Vietnam. They had a son, but the officer returned to the United States and married. The year was 1967.

Earlier this month, Do Thi My, now 37, sat in Ho Chi Minh City's Tansonnhut Airport with her son, a strapping youth with light-brown eyes and obvious Caucasian features.

All she had to indicate her son's parentage were pictures of the father and some letters he had written. The documentation was insufficient. Last April, U.S. authorities had rejected her application to emigrate to the United States.

Now she and the boy, Do Thu Son, were waiting to board a flight to Bangkok under the U.N. Orderly Departure Program on their way to settle in Maine, where a family had agreed to sponsor them.

One of thousands of children fathered by Americans in Vietnam, Do Thu Son had qualified for entry into the United States as a refugee--an indirect result of new U.S. legislation that took effect in January aimed at facilitating the immigration of Amerasians.

"I don't want my son to stay here," Do Thi My said shortly before leaving Vietnam. "I want him some day to meet his father."

Their case and other similar ones help demonstrate the extent of U.S. assumption of responsibility for the Amerasians left in Vietnam. It is also one of the few bright spots in an otherwise bleak outlook for Vietnamese refugees and those who are trying to leave.

The Hanoi government has increased its cooperation with the Orderly Departure Program and the effort to bring out Amerasians, allowing the United States this month to post a second official at the office of the U.N. High Commissioner for Refugees outside Ho Chi Minh City. Officials there say the move should speed up departures even more.

In fact, the largest group of Amerasian children to date is scheduled to fly out to Bangkok today.

A U.S. Embassy spokesman in Bangkok said Wednesday that the 151-member group would include 85 Amerasian children, nine of whom are U.S. citizens, plus 15 ethnic Vietnamese children. He said it was the fifth such flight since the Vietnamese authorities began allowing groups of Amerasian children to leave last September and would bring to 181 the number of Amerasians flown out in these groups. Others have left individually on the regular Orderly Departure flights.

According to the latest U.S. statistics, 75 children who are American citizens remain in Vietnam, along with 5,601 other Amerasians whose cases are on file with U.S. authorities. American officials say they probably could find at least 5,000 more to file, but estimates of the total number of Amerasians in Vietnam vary widely.

According to Nguyen Quang Phong, a member of a government working group on refugee matters here, there are 16,000 Amerasians left in Vietnam, of whom 2,000 have applied to leave.

Operation California, a private U.S. relief group, uses an estimate of 20,000 to 25,000 Amerasians, and others have cited figures up to around 50,000. A major difficulty is matching the Vietnamese list of Amerasians eligible to leave with the American list of those it will accept.

U.S. authorities have 96,000 active files on Vietnamese families for emigration to the United States under the Orderly Departure Program. Many cases were filed by U.S. residents on behalf of relatives in Vietnam, including one by a woman whose son was listed as missing in action in 1968. "A number of our files are more in the nature of insurance policies," one U.S. official said.

Since the Orderly Departure Program began in July 1979, 27,000 Vietnamese have flown out, of whom 8,500 went to the United States. Now refugee officials expect the U.S.-bound percentage to increase.

The U.S. government "finally agreed to accept the Amerasians on a refugee status," easing the way for many who were not considered American citizens or who lacked adequate proof or documentation to qualify under immigration rules, said Thomas Malia, a U.S. consular official attached to the U.N. refugee office here.

The new ruling allows U.S. officials to qualify children as refugees precisely because they are Amerasians. This allows more children to go to the United States even though their mothers may never have been married and lack petitions filed by the fathers. In effect, it makes a child the principal applicant rather than a "derivative category" of the mother's application as before.

Among the beneficiaries of the new rules are Pham Thi Theyet, 38, a former translator for a U.S. AID pacification study group, her 14-year-old Amerasian daughter, Bao Tran, and two children by a Vietnamese father. She has only an old Texas address for Bao Tran's father and does not expect to meet the man again.

Other applicants at the U.N. office included Nguyen Thi Thanh Loan, 40, and her blond 12-year-old son, Nguyen Huu Loc. She identified the boy's father as Max Herron of Marlette, Mich., and said she last saw him in 1973 when he was a civilian working for a truck company in Saigon. She said he has since been married and divorced, and she plans to join him. The boy, however, is more reticent. "Sometimes he says he wants to go because he misses his father," the mother said. "But sometimes he says he's scared because he has no friends there."

According to Malia, a lot of the Amerasian mothers accepted these days were maids or cooks. He said former prostitutes are not disqualified: the question is never asked.

Still, many Amerasian children remain cut off from U.S. application procedures. Some are among the thousands of orphans in Vietnam, a large number of whom roam the city's streets except on occasions when, as during a visit by a dozen foreign journalists, they are kept out of sight by authorities.

According to Richard Walden, the director of Operation California, one orphanage he visited held 400 children, including 28 Amerasians. He said that the government budgeted only 45 dong $4.64 per child per month for food and that hardly any money was available for clothing or medicine.

While refugee officials on all sides continue to pursue the Orderly Departure Program, there are traces of some discomfort with the concept behind it. "Here for the first time the UNHCR is involved in creating refugees," one U.N. official said. "We are helping people to leave their country."