Hundreds of jobless Washington-area residents have recieved unemployment compensation checks late, including some who say they have been without rent and food money because their payments are four to six weeks overdue.

The late payments have come since the District of Columbia government introduced a new decentralized system for taking applications and a computerized system for making payments.

Matthew Shannon, deputy director of the D.C. Employment Services Department, said yesterday that the number of late payments has been educed to a "150 to 200 out of 35,000 persons on the jobless rolls, and all of those should be cleared up by next week.

One major problem, Shannon said, is that the records of some applicants -- notably Maryland suburbanites who qualify for city compensatin payments because they lst worked in Washington -- were sent to the wrong offices.

On Aug. 3, the department closed its central unemploymnet compensation office at 300 C St. NW and transferred all of its business with the public to five centers in outling neighborhoods.

Outside one of them, at 1319 H St. NE, a half-dozen applicants yesterday told a reporter of recurring problems of late checks.

"We have to borrow to buy food, and when the checks finally come, we owe it all to the people we borrowed it from," said Gloria Green Holmes, the mother of a young daughter, who lost her job at the Agriculture Department and is qualified for $89 weekly in unemployment compensation.

"And what makes it worse is that we can't apply for food stamps because the computer says we're receiving [unemployment] compensation and we're not qualified," she said.

Her husband, Richard Holmes, also lost his job at Agriculture and is qualified for a $196 weekly jobless pament. He said his checks, too have been consistently late since the new system went into effect.

One man, a former D.C. special police officer who lost his job in a reduction in force and asked that his name not be printed, said that his checks have been 10 to 15 days late since the new system began. A burly six-footer, he rode to the compensation office on his son's junior-sized bicycle. "No money to put gas in the car," he explained.

Under the old centralized compensation system, recipients reported in person to headquarters each week on their efforts to find new jobs. They were then certified to receive checks, which they picked up a few days later.

Under the new system, those on the rolls are sent computer cards they are told to fil out and return each time they receive a check. If the department receives the card by Tuesday, the check should be written and mailed by Friday, Shannon said.

While Shannon sought to minimize the extent of the problem, Kathy Tollerton, a Carter administration appointee who lost her job as a congressional liaison last spring, said she was among at least 100 people with check problems lined up Wednesday at the Petworth unemployment compensation center at 4120 Kansas Ave. NW. She said she has received no checks since two weeks before the new system went into effect.

Those in line were told, she said, to go home and await a telephone call.

Shannon said yesterday that the Petworth center has fully caught up and that its backing of unissued checks has been eliminated.

One problem, Shannon said, is that assignments to the five centers were made on the basis of applicants' home ZIP codes. As his department was in the midst of making assignments, the U.S. Postal Service -- at the urging of Mayor Marion Barry -- eliminated all D.C. ZIP code zones that exteded into Maryland and assigned new numbers to the Maryand areas.

This, Shannon said, created confusion in sending applicants' records to the proper office.