When Rachel Anderson, a 50-year-old welfare mother with two adult daughters and six grandchildren, received notice last summer that the house she was renting on Willard Street NW would be sold and renovated, she had visions of being evicted with no place to go.

But when the family moved last December from 1767 Willard St., NW, Mary and Juergen Haber, the new owners of the house, had helped the Andersons solve their most pressing problems.

At a cost of nearly $1,000, the Habers secured three apartments for Mrs. Anderson and her two daughters at a low-income apartment complex at 2523 14th St. NW. The Habers paid a $135 security deposit on each apartment and put down another $135 on each unit as the first month's rent.

In addition, the developers paid the family's moving expenses and helped Mrs. Anderson find work as a cleaining woman.

Historically, property owners here and around the country have been free to buy and sell houses and apartment buildings without worrying about their tenants' future housing needs.

In the last year, however, as the back-to-the city movement has gained momentum, displacement of inner-city poor families and elderly renters on fixed incomes has become a major concern of local politicians representing changing neighborhoods.

While many tenants are still evicted without assistance, a small but growing number of developers in Washington - like the Habers - are willing to pay the costs of relocating poor families in order to promote a positive image of inner-city realtors engaged in residential rehabilitation.

By offering assistance, these developers are also hoping to ward off government intervention, such as a strict anti-speculation tax that has been introduced before the D.C. City Council. The proposed tax would make it unprofitable to buy, rehabilitate and sell residential property.

Recently, the Senate Banking, Housing and Urban Affairs Committee held public hearings on the problem of neighborhood displacement in major U.S. cities, noting that the increasing movement of middle-class families back into the inner-cities is rapidly creating a relocation crisis for the poor.

"The save-the-neighborhoods movement has come of age," said Sen. William Proxmire (D-Wis.), chairman of the committee. "Now is the time to ask - Save the neighborhoods for whom?

"Will the increasing pace of neighborhood revitalization yield healthy, diverse communities with a mix of race, age and income." he asked. "Or will it merely dislocate the old, the poor and the black residents of older neighborhoods which are newly attractive to young professionals?"

In Washington, where the number of poor families displaced this year as a result of renovations is expected to be in the thousands, evicted families are often left on their own to find new housing and relocate themselves.

"We are swamped with calls every day from people out on the street trying to find a new place to live," said Roosevelt Adams, director of the United Planning Organization office at 11th and U Streets NW, in a community where large-scale displacement has proliferated in recent months.

"We help these families the best we can," Adams said. "But the low-rent housing these people can afford just isn't there."

"When I came to the City Council in 1975, only two areas in my ward were heavily affected by speculation," said Councilmember David Clark. "Now virtually every sector of Ward I is involved in speculation and displacement to some degree." Ward I encompasses the Dupont Circle and Adams Morgan sections of the District.

Under Clark's recent proposal, a heavy tax would be imposed on profits from the quick sale of residential property. The tax would be greatest if a buyer sold his holdings immediately after purchase and would diminish the longer the owner maintained posession. Th tax is designed to put commercial rehabilitators out of business and thus slow down the back-to-the-city movement.

The District of Columbia government does not now have an official mechanism for either slowing down residential rehabilitation or for relocating families displaced by private developers.

Although some families are assisted in their search for new housing by developers, many other low-income families madehomeless by real estate speculation are left on their own to find new housing of a size and price they can afford.

Louis Watson, 57, recently received notice that he and his wife must move by Sept. 16 from their small apartment at the Whitelaw Hotel, a dilapidated apartment building at 13th and T Streets NW.

The building, which has been cited for more than 300 D.C. building code violations, is being shut down by its owner, Talley Holmes Jr. He said the building may later be renovatied into condominiums or luxury apartments.

But the Watsons, like a dozen other poor families who have been asked to vacate the building, have been hard pressed to find a new apartment that can match the $65 a month rent they now pay.

"Mr. Holmes has found me a place at 17th and U Streets NW. But it costs about twice what I'm paying now," said Watson, who lives on the $177 a month he receives from Social Security. "I don't know if I'll be able to afford the other place."

George Newton, 48, a disabled veteran and the father of three, who also lives at the Whitelaw, said he has also been looking for another apartment without success. Currently Newton said he pays $90 a month for a two-bedroom apartment.

"We haven't been able to find another apartment that even comes close to that price," said Newton. "Everywhere we go, the real estate people tell us that it's going to cost close to $200 to get two bedrooms."

The Washington Residential Development Coalition, a group of about 300 inner-city housing speculators,realtors, developers and restorers, has drawn up plans for a relocation project, which the group hopes would do away with the need for the City Council's proposed anti-speculation legislation.

Under the plan, builders would pool their funds and buy housing to sell or rent to displaced families. According to J. Gerald Lustine, president of WRDC, the group's project - which is still primarily in the planning stage - could eventually accomodate all of the city's displaced poor.

"We recently purchased the first two lots for the project at a total cost of $5,593," said Lustine, who owns Lustine Realty. "We would like to build two townhouses which would be either rented or sold to a relocated family at a modest price."

Lustine said that any profits from rents or sale of the "relocation" houses would go back into a fund to buy additional houses for other relocated families, making the project self-perpetuating.

"We would like for the city to come along, look at our project and say, "You're doing a good job. We'd like to help the project by giving you some of our boarded-up houses,'" said Lustine.

"If we could get boarded-up houses from the city and do a low-cost renovation," he added, "then we could sell a nice townhouse to a displaced family for around $20,000. And that's not bad."

Since 1975, the Habers have purchased seven houses for renovation and eventual sale on Willard Street NW. Four of the houses were vacant at the time they were purchased, according to the Habers. But the other three were ocupied by low-income families.

"When we purchased the occupied houses, we told the families living there not to be afraid of us, that we would do all that we could to help them find another home," said Mrs. Haber, 34, who quit her job with an business of helping find a better place to live."

The Habers, who are white, moved in 1972 from an apartment in Greenbelt to another apartment at Connecticut Avenue and L Street NW.

"We were tired of the two hours a day it took to commute to jobs down-town," said Haber, who said he is a freelance editor. "We wanted to live in the city where we could use those two hours to do other things."

Among the things the Habers did was to buy and renovate their own residence on the 1700 block of T Street NW. Their work on the three-story brick rowhouse triggered their deeper interest in renovations on a larger scale, according to Mrs. Haber.

The Haber said they initially plan to rent their renovated houses, which are divided into two rental units, for between $400 and $500 each. When real estate prices go up, the Habers said they will sell the houses, which cost them more than $90,000 to buy and renovate. They say they must sell the structures for more than $120,000 to recover their expenses - including the cost of family relocations.

In another approach to the problem, Donald G. Gray, of Metropolitan Properties, said he went to a tenant's home earlier this year with plans to evict the family. Instead, Gray said, he convinced the family it was to their advantage to buy the house rather than move out of it.

"I sat down with pencil and paper for three hours and showed them that they could afford to buy the house. The mother and son earned $25,000 between them," Gray said.

Gray, who had brought the house four months earlier for $22,000, sold it to his tenants for $35,000. He said he could have sold it for another $10,000 on the open real estate market.

"I was more interested in seeing this family own their own home than I was in making money," said Gray.

"This family had taken care of the house. They could afford it and I thought they ought to be given a chance to buy it."

The house, a three-bedroom brick rowhouse on the 3500 block of 11 th St. NW, was purchased by Wille Mae Samons, 64, a custodian employed by the federal government, her son, William, 22, a D.C. government pipe fitter, and her husband. Samuel, 70, a retired construction worker.

"I had always dreamed of my family having a house that we actually owned," said Mrs. Samons. "But it never seemed like we could afford a house." Even after Gray offered to sell her house for $35,000. Mrs. Samons said she decided to price other houses in the neightborhood in search of a cheaper one.

"We looked at 10 other houses. All of them were going for $46,000, $47,000 or $55,000 and they were no better than ours," she said.

When the samons finally decided to buy their house, they expected to have a $266 monthly mortgage payment. Instead, the family, which paid only $189.50 for rent previously, now has a montly mortgage payment of $314.

"It seems like a lot of money," said Mrs. Samons. "But when I send off a payment, I try to think about the equaity. I'm not buying a house for a landlord, I'M buying a house my grandchildren can call home."

Although an increasing number of displaced persons are getting some form of assistance, most still get no help at all.

In 1974, when John S. Weaver Jr. purchased a huge Victorian rowhouse on the 1300 block of Rhode Island Ave. NW., 35 persons lived there. Today, only Weaver, a dance instructor and a bachelor, occupies the 15-room structure built in 1885.

"It was essentially a welfare house run by a slum landlord who rented rooms for $75 a month," said Weaver, 37. "Living conditions were awful. There were supposed to be only two or three to a room. But sometimes whole families crowded into a single room."

Weaver, who is currently working several hours a day to restore the house to its original elegance, said he gave the roomers three rent-free months to find another home.

"I knew it would be hard for a lot of them to find housing. And I don't know if they all did or not," said Weaver, who moved to Washington from Arlington, where he lived in an apartment. "But I'm not a speculator. I bought the house to live in."