One day last month the realtor who manages the Alexandria townhouse that Albertine Martin and her husband have rented for the past 12 years paid an unexpected visit and began inspecting and measuring the rooms. "I figured there was something on her mind," Mrs. Martin recalled, "but I got no good answer."

The answer came in the form of a brief note two weeks later: "This is to advise you that you must vacate 1303 1/2 Prince Street no later than January 31, 1978."

So last Friday Mrs. Martin, who baby-sits during the day, and her husband, a part-time construction worker, moved out of their home and into a one-bedroom, $195-a-month apartment on Abingdon Drive in Alexandria.

The Martins found their new home through the help of a refiend, but they were upset about having to leave the neighborhood they knew so well and the comfortable house they had recently repainted at their own expense.

"I don't think it's fair," Mrs. Martin told a visitor recently. "It's not fair for the simple reason that I don't know where the lower class is going to go."

The two-story house where the Martins lived is one of three red brick town houses in the 1300 block of Prince Street that are being sold by their owner after he renovates them.

The housing problem for the Martins is similar to that being experienced by other families in the expanding Old Town section of Alexandria, the enclave of 100 to 200-yard-old homes along the Potomac River and several blocks to the west.

Old Town traditionally has been confined to the east side of Washington Street.Now, despite the wishes of many residents west of Washington Street to continue to rent their existing homes, developers are giving them eviction notices, renovating the sometimes deteriorating homes and then selling them to others, at much higher prices as part of the expanded Old Town.

The Old Town experience is one that has occurred elsewhere in Washington on Capitol Hill, in Adams-Morgan and other communities.Lower-income blacks are often moved out of the homes they have rented for years as developers move in with their hammers and saws for renovation work. The refurbished houses often are sold to higher-income whites.

In Alexandria, the result has been an increase in real estate speculation west of Washington Street and pressure on the area's long-time residents, many of whom are elderly and live on fixed incomes, to sell their property.

Four years ago, when the Old Town Civic Association proposed that the City Council extend the boundaries of the Old and Historic District (Old Town's official name), the suggestion generated an outcry from residents of the surrounding community.

A. Melvin Miller, then chairman of the Alexandria Redevelopment and Housing Authority, warned at the time: "If you extend the boundaries of Old Towne the same thing will happen - the real estate people will move in buy up the houses: the tax rate will go up and the low-income people who happen to be black will be forced out of their homes."

Not only was the Old and Historic District not extend, but the City Council reaffirmed its previous commitment to maintaining housing for low-income families in the city and a study was started on how to preserve downtown Alexandria.

Despite those steps, city officials, ral estate developers and residents of the community agree that Miller's prediction has come to be the dominant reality. Today, developers say, an abandoned house that is bought for $20,000 can be sold for $130,000 and up once it has been refurbished.

'It's happening at a lot faster pace than a lot of us thought likely a few years ago," says Peter Schumaier, president of the tradition-conscious Old Town Civic Association.

How fast it is happening becomes evident during even the most casual of strolls along such streets as Pendleton, Oronoco, North Alfred, and North Columbus.

A row of renovated town houses often contrasts with an empty lot across the street. A dilapidated and boarded up house sits conspicously between two freshly painted homes displaying placques that mark them as historic landmarks and may raise their sale price by as much as $10,000. Old-style corner stores and small churches are boarded up, soon to be replaced by Georgetown-style boutiques.

Middle and upper-income white professionals have flocked to Old Town in recent years because of the area's close proximity to Washington and the prestige many believe the neighborhood offers.

"It's like wearing Guccis or a Cartier watch. It's a comment on your life style," one newcomer said recently.

The expansion of Old Town has been accelerated by work on the King Street Metro station, which is expected to open in October, 1980. City officials foresee the day when Old Town could extend from the water-front to the RF&P railroad tracks, nearly twice as large an area as the traditional area east of Washington Street.

"I'm going to try to hang to my little house, but God only knows how long I'm going to be able to do it," said Ellyn Carpenter, who has lived in the same house on Oronoco Street for 27 years. "Old Town reminds me of an octopus with a whole lot of tentacles swallowing us."

Some streets have been almost completely renovated such as Prince, where the Martins live. "Every time a house gets empty they fix it up and the whites move in," Mrs. Martin told a visitor.

The whites who move in are people like Hal and Annelise JOnes, who moved to Alexandria from Chicago in August are now renting a renovated town house just half a block from the Martins.

"Living in a town like this I feel closer to Europe," said Mrs. Jones, who is from France and now works as a translator for the International Monetary Fund. She said she liked the idea of having shops, restaurants and boutiques within walking distance.

The Joneses pay $500 a month rent for the two-story house, which has two bedrooms, a living room, a large kitchen, and two fireplaces. The Martins, by comparison, pay $120 a month for a comparably sized, unrefurbished house.

That kind of rent disparity in housing prices was at the heart of a battle four years ago over the defeated proposal by the Old Town Civic Association that the boundaries of the Old and Historic District be extended to included part of the area west of Washington Street.

"It's part of the American way. You have a commodity so you pay fair market value," said Greg Golubin, an Alexandria realtor who has done business in the Old Town section.

A 2-year-old study of the downtown area financed by the National Endowment for the Arts recommended limiting the free market forces in the area by having its residents establish a "community cooperative" that would guarantee that houses would be sold to persons with modest incomes. In this way, the report said, the traditional character of the neighborhood would be maintained. The proposal was defeated in a 1976 referendum, largely because of opposition from residents of the area west of Washington Street.

Alexandria officials, while expressing concern about displacement of low-income people, say the city as a whole will benefit from the redevelopment expansion of Old Town.

"Other cities in this country would dearly love to have private forces like this," City Manager Douglas Harman said in an interview. "If this private redevelopment were not taking place," Harman added, "we would be like many other industrial cities with a tremendous tax and economic problem."

The city has established the so called Potomac East and West Conservation Districts to help property owners upgrade their homes and maintain neighborhood stability without selling homes to developers. Under a program approved last month for Potomac East, and area north of Old Town, homeowners can receive up to $15,000 to refurbish their homes and not have to pay it back. But the City Council asked its staff to continue studying a proposa lfor 6 percent interest home improvement loans.

The city has also budgeted $410,000 to acquire abandoned and condemned properties in the downtown area that are then renovated and sold to low and moderate-income persons who would not be able to afford the houses if they were being sold on the open market. The city is just now beginning to spend the money and so far no houses have been renovated or sold.

The result has been that "you have two sectors running after the same house," said Raymond Johnson, a city planning official. "The city is trying to repair it for the moderate income people and the more affluent people also are trying to buy it."

Sitting in her cramped but clean kitchen, Mrs. Martin spoke philosophically about the sudden news that she and her husband would have to go elsewhere.

"You can't beat them, so why should you try to raise a stink, especially since you're the underdog. So be it," she said.

"My kids are gone and living in Philadelphia," she continued. "And thank God they own their own homw.Nobody can push them around like this."