Six years after the federal government stopped accepting new applications for home sites under the 1862 Homestead Act, 178 families are still waiting for the Interior Department to approve their requests for land.

When Interior does complete action on those applications, it will close out the most extensive federal land transfer program in history. Over the years, the program gave nearly 1.5 million homesteaders nearly 250 million acres of land, or about one out of every nine acres of land in this country.

Under the program, the government opened up sections of the country and families could claim up to 160 acres if they were willing to work the land for at least five years.

The delays in resolving the final cases have been caused by the government's legal responsibilities, said James W. (Tim) Monroe, a Bureau of Land Management spokesman. He said that includes making sure that no one else has claimed title to the land, that it has been surveyed properly and that it has been used for agricultural purposes.

In 1976, Congress ordered Interior to stop accepting new applications and passed a new law--the Federal Land Policy and Management Act--that required the sale of unwanted public land at fair market value. Only Alaska was exempted, until 1986, but BLM officials doubt there will be any new homesteading opportunities there.

But the transfers continued. In fiscal 1981 the department transferred 11 homestead sites covering 1,085 acres (statistics aren't available yet for fiscal 1982). Of the remaining applications, 84 are in Alaska, 64 in Montana, 14 in South Dakota, 13 in Nevada and three in Idaho.

"We still get a lot of calls from people who think this program is alive, and there's someplace in the country they can get some federal land," said BLM official Jan Bedrosian. "We're trying to quell that."

The department, however, is still accepting applications for a separate program that opened 10,000 acres in central Alaska for use as home sites or commercial development.