Anthonita Dooley and her two children applied for D.C. public housing in 1975. Since then she has had three more children, and today she lives with 12 relatives in her mother's cramped public housing unit.

She and her children, two of whom are teen-agers, share a bedroom.

"I feel like giving up," said Dooley as she inched sideways between the dresser and a bunk bed. "It's disgusting with me and my kids sleeping in here, and it's depressing. I can't find any place out there where I can go that I can afford or that takes children. When I call the housing department, they just tell me I'm on the list. I knew that 10 years ago."

Dooley is one of the 11,056 applicants on the city's public housing waiting list. Most -- including 4,583 families seeking two-bedroom units and 3,340 waiting for three-bedroom units -- have been told they will have to wait about seven years for an apartment.

At the same time, however, there are hundreds of apartments standing vacant. In March, for example, there were 2,066 vacant public housing units, giving the D.C. Department of Housing and Community Development a vacancy rate of 17.58 percent.

It is one of the highest in the nation and more than the combined public housing vacancy rates for Baltimore, Philadelphia and New York City. In New York alone, 600,000 people live in 174,881 public housing units, yet only 115 units, or 0.07 percent, are empty.

The District's housing department has for the past decade been slow to repair vacant units and to complete multimillion-dollar remodeling projects. Efforts to correct the problems resulted in a cycle of deteriorating units.

While maintenance workers were detailed to repair vacant units, routine maintenance work went undone in occupied and aging buildings, gradually causing major structural problems. The department, operating with limited staff, became selective; the easier problems were fixed, and work orders stacked up. More units became vacant and more public housing projects started to need major renovation. Authority maintenance workers have also come under criticism as being inefficient and not responsive to tenant needs.

The housing department is apparently caught on a treadmill as it attempts to repair a backlog of vacant units while restoring the estimated 40 that become vacant each month. The department, which operates 11,749 units for 60,000 tenants, is also seeking more money for comprehensive modernization projects. Housing director Madeline Petty, while acknowledging problems, said the authority is on its way to correcting them.

A U.S. Department of Housing and Urban Development task force reviewing the D.C. housing authority's operation is also examining the vacancy rate. Excluding 1,229 vacant units the authority has scheduled for complete modernization, the District's vacancy rate is 11 percent, nearly double the rate that HUD has established as acceptable for troubled housing authorities.

Jacqueline Aamot, HUD executive assistant to the assistant secretary for public and Indian housing, said that although the District's vacancy rate is not the nation's worst, excessive vacancy rates anywhere are considered a "big problem."

"We pay an operational subsidy for those units," Aamot said. "The money is appropriated to pay for shelter, and when units are boarded up it is like the money is going for nothing."

HUD, in its 1984 audit, estimated that the District's annual rental income loss attributable to vacant units was $1.4 million.

Some of the current vacancies date to the late 1970s. In the Valley Green complex in Southeast Washington, one unit now being repaired has been vacant since 1977, according to housing records. Some were vacated more recently. Three units that became empty in November 1984, April 1985 and July 1985 were still listed as vacant last month although housing records show that each is in good condition and in need of minor repair.

Petty said the major problem behind the department's high vacancy rate has been a shortage of staff and money. Reducing that rate has been made a priority, she said, adding that it is too early to judge the department's progress because her solutions are now being implemented.

Petty has placed the authority's modernization projects under a new administration. The authority had been criticized because it completed just three of 10 modernization projects undertaken since 1977 with $132.7 million in federal and District funds.

Ben Carter, acting director for the new modernization administration, said delays ranging from six months to several years at some projects were caused by a shortage of property managers, a lack of money because the department underestimated construction costs and the inability to relocate tenants quickly.

Carter said 36 people will be hired to provide technical assistance to projects, and official cost estimates will be obtained before the construction funds are requested so that "we won't look like the money is sitting here."

Petty has also begun a fast-track repair program, in which private contractors are hired for some vacant unit repairs previously assigned to the maintenance staff. D.C. deputy housing director Dreck Wilson said vacant units will be repaired in one to 30 days under this program. Private contractors will do major work, minor repairs will be made by the property staff, and a housing task force of 50 to 70 workers will do moderate repairs.

Since December, the housing department has repaired 347 of the 550 units it had targeted, and it has earmarked another 474 units for repair. Among the repairs completed were 23 of 30 vacant units at Kentucky Courts in Southeast and 38 of 43 units at Claridge Towers in Northwest.

While some apartments that became vacant in January remained vacant at the end of March, Petty said she is delighted with the department's progress and plans to request an additional $12 million to $15 million in city funds for the repair program.

"There are always in a housing authority, on any given day, vacant units," said Petty, who became housing director in 1984. The fact that the authority is now able to have a contractor on the job within three months of its becoming vacant is a complete turnaround in efficiency, she said.

Even if the District's housing department could reduce its 18 percent vacancy rate to zero, it is clear that it could not house all of the families on the waiting list. But for many of those families, every boarded-up public housing unit serves as a wrenching reminder of their dismal life styles.

Janice Gore, who says she has waited 10 years for a unit, hopes to hear news of an available unit any day.

In the seven years since she submitted an application, Gore, 32, said that she moved nine times. For the past three years, she and her children have lived in a homeless shelter.

"I was homeless so much that my oldest child didn't start school until she was 8 years old," said Gore. "Me and my kids have suffered a lot. We've slept on floors, we've been without heat, we've been without water and without food. I've had a nervous breakdown, and I've learned you have to expose your life to get help."

George H. Mernick, an attorney with Hogan and Hartson, represents a woman who is suing Mayor Marion Barry and Petty because she was denied a spot on the public housing emergency waiting list after being evicted from an apartment.

It generally takes applicants on the emergency waiting list about a year to get an apartment.

"It just seems to us that the number of vacancies is so great that they can't be justified when they turn emergency people away," said Mernick. "In light of the human problems involved, the obvious answer, with all the vacant units, is to fix them and don't send mothers with four and five children to motels and shelters."

Some vacancies have created dangerous situations for public housing tenants and a financial burden for the housing department.

Each day that Christine Hazelwood walks out of her apartment at the Valley Green public housing complex in Southeast, she stares directly into a five-bedroom unit that has been vacant since 1982. The walls have been bashed in by vandals, a hole in the floor provides a view of the empty apartment below, and children sent to empty trash have begun throwing it into the vacant unit.

"Junkies go in there to use drugs, and I'm afraid for my girls and I'm afraid for myself when I come and go," said Hazelwood. "The housing department knows about it, and it's the maintenance people who keep taking the board off the door."

Paulette Lanham says she waited for a public housing unit for 10 years before she moved into a Highland Addition unit sandwiched between two vacant units. The unit above her is unlocked, and as she talked about the three men who sleep there, one of them stopped by to borrow a match. Lanham became incensed.

"One morning at 4 a.m., I smelled smoke and chemicals coming through my door," said Lanham. "I rushed upstairs because I thought the apartment was on fire. The three guys were up there cooking PCP."

There are financial considerations. HUD in its audit noted that a two-bedroom unit at Highland Addition that became vacant in September 1981 could have been fixed for $500, before vandals caused $1,200 in damage.

Since the HUD report, the vacancies at Highland Addition have grown from 22 to 35 and the vandalism estimate for 21 of those units is $84,000. The vacant unit highlighed in the HUD report remained vacant at the end of March, and the vandalism damage had increased to $2,000