About 6,800 D.C. residents entitled to receive unemployment compensation failed to get their checks over the last two months because of a computer foul-up in the city's troubled Department of Employment Services, officials said yesterday.

Meanwhile, the department did nothing to inform the qualified recipients that the checks -- which some persons said they were told would arrive 7 to 10 days -- would be slow in arriving, according to employment services spokesman Adolph Slaughter.

As a result of the computer malfunction, the agency last week had to hire 14 additional workers to laboriously type and address the checks, which should have been distributed in September and early October, Slaugher said.

"It's going to be straightened out," he said. "I wish I could tell you when."

Slaughter blamed the delay on a malfunction in the department's computer system, which for some reason refused to write the checks in the correct amounts. The problem was discovered several weeks ago, he said, but its cause remains a mystery.

The mix-up is only the latest for the beleaguered department, which was involved in heated controversy earlier this year because of extensive delays in getting paychecks to youths who participated in Mayor Marion Barry's summer job programs.

Last month, Barry dispatched his often abrasive top aide and chief political operative, Ivanhoe Donaldson, to serve as acting director of the agency following the resignation of department head William R. Ford. The move was seen as an attempt by Barry to take firm control of a bureaucracy with a long history of unresponsiveness.

Barry said yesterday that he was unaware of the problem in distributing unemployment compensation checks, but added, "It's a mess over there." He adknowledged that Donaldson, who could not be reached for comment, has his work cut out for him.

The delayed checks were supposed to go to unemployed persons whose initial eligibility for compensation benefits had expired, but who in midsummer automatically became eligible for between 5 and 13 weeks of additional benefits, Slaughter said.

The extra benefits became available after the nation's then-climbing unemployment rate reached a previously specified trigger point. The federal government provided funds for the extra benefits.

Slaughter said the department began notifying the 6,800 persons of their eligibility for the new benefits in early September, and asked them to register to get the extra money. Most, like former District government worker Rebecca Francis, responded promptly.

Francis said yesterday that after leaving her job as a training representative with the D.C. Apprenticeship Council in May 1979, she collected unemployment benefits for 32 weeks before her initial eligibility ran out.

She said that when she came in to sign up for the extra benefits on Sept. 15, she was told that she would receive seven weeks' worth of new payments. "They said they could just check the computer and tell whether you were qualified," she said.

Francis said she was told additional payments totaling $945 would arrive in 7 to 10 days. By yesterday, she said, she was still waiting.

" after the first three weeks I went back down to the office," she said. "I talked to a clerk, and the clerk said they had all been told that if anybody asked about those benefits to pretend they didn't know anything about it."

It took more than a week to discover the extent of the computer malfunction, Slaughter said. The computer had accurately recorded the names of those eligible, he said, but had refused to generate checks in the proper amounts. "The checks would come out, but we couldn't send them," he said. "We have to do them all over again."

"A few" of the checks with the wrong amounts on them were in fact mailed out, but Slaughter said he didn't know how many. He also said he did not know the overall amount of money that the jobless are entitled to receive.

Slaughter said the department did not try to contact the prospective recipients to tell them their benefits would be delayed because "it was just an incremental thing. Each week and each day we thought the problem would be solved. We didn't want to deflate the people."

He said department workers, including the 14 newly hired clerks, are currently sending out checks at a rate of more than 400 per day -- a tedious process begun last week. "We're doing it just as fast as we can," he said.