For nearly a year, Mayor Anthony A. Williams's message to people thinking about moving to the District has been this: Come invest in our city and become a part of its rejuvenated tax base.

So far, it's not something the mayor has done himself.

Despite a campaign promise that he would buy a house in the District, Williams and his wife, Diane, continue to live in a rented one-bedroom apartment in a high-rise across from the Watergate complex.

Williams (D) said he still plans to buy property in the city, but during his first year as mayor, house-hunting has taken a back seat to his round-the-clock efforts to improve city services and revamp D.C. agencies. That work has won him praise across the city, and some residents do not see Williams's absence from the property-tax rolls as significant.

But others do, and they increasingly are asking when--or whether--Williams intends to establish roots in a D.C. neighborhood. It's a conversation heard more often in parts of the black community, where activists say owning property can be a particularly poignant symbol of a person's commitment to the majority-black city.

"The African American middle class puts great stock in having roots in the city and attempting to establish roots in the city," said Dwight Cropp, an associate professor at George Washington University. Cropp, who was an aide to then-Mayor Marion Barry, is married to Linda W. Cropp, chairman of the D.C. Council. "For the new white residents moving in, this may not be an issue. It depends on your cultural frame of reference, your perspective and your background. But for the African American middle class, this is very important."

Cropp said that in the District, a mayor's decision to buy property--and where to buy--is loaded with symbolism and politics. For a mayor like Williams--who has lived in this area only since 1993 and has a history of not staying in a job for more than four or five years--not buying property can lead to all sorts of speculation, Cropp said.

Cropp and his wife live in upper Ward 4 in Northwest Washington, which has been home to many in the black middle-class in recent years.

"Is he here for the duration?" Cropp asked. "Lots of people are saying [Williams will serve only] one term. What is the overall commitment to the city?"

Williams won't comment on any future election plans but said he and his wife recently sold a condominium in St. Louis, so they could "make a permanent investment in the District."

"My priority the first year was working 24 hours, seven days a week to turn the government around and . . . to make a presence in the city," Williams said. "Now . . . I'll work with people to locate a home. It's our intention to buy a home and permanently reside here."

But where?

Foggy Bottom, near his current apartment? Or some other largely white, well-to-do community in Wards 2 or 3, where his residency might be viewed dimly by some in the black community? Or might Williams--who has preached economic development for Anacostia--set an example by moving to a downtrodden area east of the Anacostia River? Or would that come off as too patronizing for a mayor who is viewed suspiciously by some low- and middle-income blacks because of his moves to trim the city's payroll?

No matter which of the city's eight wards the mayor ultimately chooses, it's likely that some people will feel snubbed.

"Wherever he moves," said one mayoral aide, "he makes one-eighth of the city happy."

Said Williams, "This decision is pregnant with ramifications."

Barry recognized that when he went house-hunting in 1978, after he was first elected mayor.

Aides encouraged Barry to show his commitment to Southeast Washington by buying a home there. Barry left his Capitol Hill town house and moved to Hillcrest, a middle-class community in Ward 7, which was then an integrated community that was growing in prestige. As more blacks moved to the neighborhood it seemed to reflect the new prosperity Barry wanted the government to help deliver to black Washington.

More than a decade later, a disgraced Barry returned from prison to live in Southeast Washington's Ward 8--where his man-of-the-people theme played well--and rejuvenated his political base enough to win a council seat and then recapture the mayor's office.

Walter Washington, now in his eighties, lived in the historic LeDroit Park area when he served at the city's first elected mayor. That neighborhood, near Howard University, was once the center of the city's black middle-class life.

When she was mayor in the early 1990s, Sharon Pratt Kelly lived in an affluent area of Northwest Washington, far from the city's poorest neighborhoods. In some ways, it was symbolic of the difficulty she had in connecting with low-income residents.

Williams has had similar difficulties on occasion, although in recent months he has made a point of making more appearances across the city. Buying real estate, some activists say, would be another step in showing many residents he is devoted to the city.

"If he's planning to stay here, he should try to own property," said Paula Nickens, chairman of the D.C. Democratic State Committee. "I don't know what his plans are for the future, but if he plans to run for a second term, I would think he would purchase property here. People are talking about it."

Others, such as Phil Pannell, president of the Ward 8 Democrats, said that Williams's decision is between the mayor and his wife and that taxpayers shouldn't be telling them where they should live.

Pannell, however, couldn't resist adding this: "I would hope the mayor is holding off until his dream house is built here east of the Anacostia River."

Williams has lived in the Washington area for six years, spending about a year of that in Northern Virginia. He had worked in Boston, New Haven, Conn., and St. Louis before taking a job here in the Clinton administration and then becoming the District's chief financial officer. With the city recovering from a financial crisis, community groups and business leaders drafted the relatively unknown Williams for a successful bid for mayor last year.

Howard Croft, an official with an advocacy group called the Center for Community Change, said some of the mayor's supporters also are newcomers to the District and so may not be too concerned whether the mayor buys property.

"The mayor probably feels this is a non-issue for his base," Croft said. "There are large numbers of his supporters who do not have deep roots in the community either.

"This is a mayor who has been dogged by whether he will sink his roots anyplace," Croft said. "He could put some of these questions to rest by sinking his roots someplace. There is a whisper campaign about whether the mayor is here for the long run. It's symbolic and important to say, 'This is my town, and I'm here for the long run.' "

Williams said the decision about where to buy property in the District is very personal. He wished that the city had a permanent residence for its mayor, such as Gracie Mansion in New York City. But he's not in favor of spending any city money to buy such a house.

"It's an emotional decision," Williams said. "D.C. adopted me as mayor. I'm part of this family, and I want to make my roots here."

As for where he might move, Williams is vague--and diplomatic.

"There are so many beautiful and great neighborhoods, and that makes it a hard decision," he said. "We're consulting with people. It's something that we intend to take seriously. . . . It's not like buying a pack of cigarettes. But it's not whether [to buy a house in the District], but where."