AMERICAN troops left behind in Vietnam more than a defeated nation and tons of military equipment. Thousands of their children, born to Vietnamese women, remained to suffer not only the hardship of a war-ravaged society and that inflicted by the new political order, but the special discrimination reserved for children of mixed race as well. Other soldiers' children live in Laos, Thailand and Korea and suffer many of the same hardships. Under U.S. immigration law, such children cannot automatically enter as sons or daughters of Americans since illegitimate children inherit only their mother's nationality. In addition, many of these children do not know or cannot prove the identity of their non-Asian fathers.

Many Americans believe there is a moral responsibility to care for these children, and some members of Congress have proposed the admission of children who are acknowledged by their American fathers. But that would cover only a small percentage. Rep Stewart McKinney (R-Conn.) has proposed a more generous program. It would allow any citizen of Vietnam, Laos, Thailand or Korea, who appeared to be Amerasian and who was born after 1950, to apply for a visa. American consular officials would decide, on the basis of appearance and whatever additional evidence was available, whom to admit. Each applicant would need an American sponsor willing to provide support for five years.

Estimates of the number who would qualify vary from 20,000 to hundreds of thousands. No one can know how many would be eligible or would want to come. In any event, the McKinney bill would admit them under the regular immigration quota for children of Americans--81,000 a year--so the total number of new immigrants would not be raised.

In considering Mr. McKinney's bill, the House immigration subcommittee made some important changes that generally preserve the spirit of the bill and eliminate some possible problems:

* The panel limited the program to children under the age of 21, acting on the presumption that street waifs are of greater concern than adult middle-aged offspring. The occasional desired children over 21 could be covered by private legislation.

* Determining that a five-year sponsorship was not sound for young children, the subcommittee provided that in cases where children under 16 were not adopted, sponsorship must be guaranteed until age 21.

* Cambodia was added to the list of countries covered, and the requirement that the American father be a member of the armed forces was eliminated.

* The subcommittee removed the annual numerical limit on the number of children who could enter under this program, while adopting a time limit of 10 years for the program as a whole.

A caution is in order. Though Vietnam has been reluctant to allow Amerasian children to depart, recently the foreign minister has hinted that public interest in the United States may persuade his government to relax its policy. Such a change would be welcome, but it is important that Americans retain control over the process. Recent experience with Cuba has made plain the costs of allowing a dictator to decide which of his countrymen he will send to the United States. This program, like the broader orderly departure program for Vietnamese refugees, must preserve Washington's right to make the crucial decision on which applicants come to these shores.

The Senate will consider major immigration reform later this month and shortly thereafter will take up the Amerasians. Rep. McKinney deserves commendation for driving this issue to the public attention. The House subcommittee has improved his bill. It should be passed.