In 1981, Mayor Marion Barry pledged to spend $61.4 million to renovate one-third of the city's public housing units within three years. Today, no work has begun on most of them.

City housing officials attribute the delays to difficulties in relocating tenants while their units are being remodeled. The city recently started to try to correct that problem by asking private landlords to rent units temporarily to the city for use by the public housing tenants. But the mayor waited until May to request that $125,000 be spent this year on that program, and the city announced it just three weeks ago.

Meanwhile, many of the tenants who live in apartments awaiting rehabilitation said in recent interviews that they have grown accustomed to poor plumbing, broken appliances, holes in ceilings and insufficient heating during the winter.

The city government operates about 12,000 public housing units in 52 projects around the city. Housing nearly one-tenth of the city's population, the D.C. government is the city's largest landlord. The overwhelming majority of public housing tenants are elderly women or single mothers with small children who receive public assistance.

Only one of those renovation projects -- James Creek Dwellings, at First and O streets SW, has been completed. East Capitol Dwellings and Lincoln Heights, both in far Northeast, are under construction. A few units at Benning Terrace in Southeast are under construction. And architects are working on plans for the renovation of the remaining five apartment complexes, consisting of 1,520 units, but it is uncertain when construction will begin.

"I'm the first to admit that some of our public housing units are falling down and not fit to live in," Barry said four years ago in announcing the renovation program. He described it as the most comprehensive and expensive efforts ever undertaken by the city to modernize and repair a major part of its public housing.

Beverly Pelzer, whose mother lives at Richardson Dwellings at 53rd and Clay streets NE, said city housing authorities have been promising for years to rehabilitate the tattered brick apartments.

"They [housing officials] told everybody they have to move out by August because they were going to start fixing the place up," said Pelzer. "A lot of people have already moved out, but they haven't done any work yet. I don't know when they're going to get around to fixing this place."

The federal government and the District have earmarked $7.6 million for the renovation of Richardson. Two years ago, the interiors of 86 units at Richardson were repaired or remodeled, including installation of a few new kitchens and bathrooms. But the majority of the 190 units remain dilapidated, with peeling paint and problems with plumbing and electricity.

To deal with the problem of providing temporary housing for tenants while their apartments are being upgraded, the city announced three weeks ago that it was seeking landlords to participate in a new Private Leasing Program. The City Council last week approved $125,000 for the program, and the mayor put $600,000 in the fiscal 1986 budget for the program. None of the money has been spent.

City officials said the problem of finding temporary housing for displaced tenants has caused the major delay in the work. In the early days of the renovation program, the city moved tenants to other public housing projects. Now the city is willing to pay private landlords to house the tenants temporarily until the units are completed.

Under the new program, the city would select landlords willing to lease units at a "fair market value" as determined by the U.S. Department of Housing and Urban Development. Relocated tenants would pay 30 percent of their income in rent, as they do now in public housing, and the city would pay the difference between that amount and the actual rent.

"The goal is to relocate approximately 75 families," explained Oliver Cromwell, spokesman for the city Department of Housing and Community Development. Residents of 1,520 units in five apartment complexes will need to be relocated by the city before repair work can begin, he said.

Fifteen landlords expressed interest two weeks ago in the program, but none has agreed to the plan, Cromwell said.

"There's a relocation problem we had at [two housing projects]; we did not have the necessary resources to relocate people," said Benjamin Carter Jr., who supervises the public housing renovation program. " . . . So the relocation problem is what's caused us to get behind schedule on a lot of these projects."

But Florence Roisman, counsel to the National Housing Law Project, which represents public housing tenants in disputes, said there are more than 1,590 vacant housing units in the District.

"Someone should ask those [District] housing officials if it ever occurred to them to fix up the units that are standing empty and then relocate people into the empty units," said Roisman. "There are plenty of empty units" in the District, she added.

According to Cromwell, nearly 600 of the city's vacant public housing units do not meet building code requirements. "Because of fire hazards and minor repairs that need to be made, we can't move people into them," he said.

Madeline Petty, director of the city housing department, said that HUD wants cities to hold down the vacancy rate in their public housing to 3 percent.

The District's vacancy rate is more than 13 percent, compared to Baltimore, which has a vacancy rate of less than 1 percent.

"The rapidity at which we can restore vacant units is in direct proportion to the funding available," said Petty. "The problem is finding the money to repair these units."

Because of lengthy delays, nearly 400 apartments have been vacant at the Lincoln Heights project in far Northeast for more than a year. At East Capitol apartments, where work was to be finished more than two years ago, nearly 60 units are vacant, partially because of subsurface water damage delaying construction, according to Carter.

Families were moved out of 214 units at Greenleaf Gardens two years ago, but no repair work has begun.

Most of the city's housing projects awaiting renovation are 30 to 40 years old and have had few major repairs since they were built.

Here is the status of the nine housing renovation projects that are running one to 3 1/2 years behind schedule, based on information provided by the city housing department:

*James Creek, 239 units at First and O streets SW; completed in October 1984 nearly two years behind schedule.

*East Capitol, 577 units at East Capitol and 58th streets NE; 60 units vacant and 10 under construction. The project is several years behind schedule.

*Lincoln Heights, 440 units at 50th and Blaine streets NE; 86 units completed in December 1984; 354 units vacant and under construction. The project is at least two years behind schedule.

*Richardson, 190 units at 53rd and Clay streets NE; architectural plans in progress; no construction started. The project is nearly two years behind schedule.

*Barry Farm, 444 units at Sumner and Wade roads SE; architectural plans completed; no construction started. The project is more than two years behind schedule.

*Benning Terrace, 274 units at 47th and G streets SE; architectural plans completed; construction started on a few units. The project is more than two years behind schedule.

*Highlands, 208 units at Condon Terrace and Atlantic Street SE; architectural plans in progress, no construction started. The project is running nearly three years behind schedule.

*Kenilworth, 422 units, and Parkside, 42 units, both at Kenilworth and Douglas avenues NE; architectural plans in progress; no construction started. The project is more than 3 1/2 years behind schedule.

*Greenleaf Gardens, Third and M streets SW, 213 units; emptied of families two years ago and slated for conversion to a building for senior citizens and the handicapped; architectural plans in progress; no construction started. The project is running more than 3 1/2 years behind schedule.