Sixteen months ago, Time, Inc., announced plans to move its Time-Life books division from New York City to Alexandria and the company subsequently did so.

Two months later, another New York firm, Mobil Oil Corp., said it was moving the offices for its marketing and refining division to Fairfax County.

Last month the American Telephone and Telegraph Co. announced plans to move its regional lines department from the District of Columbia to Fairfax.

Washington suburban officials point to these moves as evidence of the growing attraction of the Washington area for large corporation that are leaving the cities for the suburbs.

There are an estimated 26,000 businesses in the Washington area. No one knows exactly how many businesses have moved into the Washington area in recent months, but corporation recruiters say that the region's jurisdictions are increasingly successful in persuading companies to locate offices here. Every Washington-area government has beefed up its efforts to attract firms that will broaden its tax base and increase employment opportunities.

Officials in Fairfax County are promoting the county's available space for corporate headquarters and other businesses by advertising in the Wall Street Journal and New York Times. They also plan to run ads in a Japanese publication for heads of large corporation and two other trade magazine as part of their $14,000 advertising campaign.

The ads mention TRW and the American Automobile Association which are already in the county, and will eventually mention AT&T and Mobil, two of the companies planning moves to the county. "There's no question that one satisfied customer brings another," said David A. Edwards, head of the Fairfax County Economic Development Authority.

In Prince George's County, this year's $20,000 budget for economic development is double that of last year. The county has taken on the name of "Baltington" in ads that appear in magazines like Fortune and Forbes as part of a recent $115,000 advertising campaign.

Prince George's officials said last week's lifting of the seven-year-old moratorium on new sewer connections in the eastern part of the county also is expected to attract more businesses.

'For the first time, the county is going to have sewer service for some areas that have very fine locations," said George H. Smith, a county economist.

Officials in Montgomery County are planning what they call "a more aggressive program" of luring businesses to the county including sending representatives in New York, New Jersey and Chicago to meet with corporate executives.

Even localities like Alexandria that have very little, if any money budgeted for economic development are joining with the local Chamber of Commerce to try to attract firms.

"We want to destroy the myth that Alexandria is completely built up," said Donley F. Hunt, chairman of the city's Economic Development Office.

A few of the local jurisdictions for the first time are working on a regional program to promote the entire Washington metropolitan area. These recruiters meet monthly, to discuss ways to improve their recruitment techniques.

"Our viability is tied to the (region's) viability," said Frederick Agostino, deputy director of the Montgomery County Office of Economic Development.

Many suburban officials expect the expanding Metro subway system also will help attract more businesses to their area. "We are looking to capitalize on the transportation link with the District of Columbia," said Hal Glidden, an Arlington official. "We expect to see a sufficient amount of new business coming into Rosslyn and Crystal City (which now are served by Metro)," he said.

The District of Columbia already has replaced New York as the capital of trade associations as these organizations try to get closer to the federal decision-makers.

One indicator of the business influx in the suburbs is the business directory put out by the Montgomery County Chamber of Commerce. In 1973, there were 4,200 businesses listed in the directory. Today, the directory contains the names of 10,800 firms.

The reasons for corporate moves to the Washington area are often the same. Company officials often cite the close prozimity to the federal government, the spacious office accommodations and room for expansion, lower taxes (especially in the case of New York firms), and convenient transportation.

Some companies, especially large corporations, are very secretive about their moves here.

Edwards, head of the Fairfax development agency, said his staff was contacted by three persons working on behalf of a single firm, which he later learned was Mobil.

He said the first contacts concerning Mobil were made in 1974, but the company did not announce its intention to move to Fairfax until May, 1976.

Edwards said companies often want to remain anonymous to avoid driving up price of the land they may want to buy and to avoid alarming their employees until the move is final. He said some company officials have used fictitious names in dealing with his office.

Some company employees are happy to follow their job to the Washington area. Others prefer to stay where they are and give up their job. Still others come, but later regret the move.

Mel Scott, director of the photography for Time-Life books division, is in the last category. Scott followed his job to Alexandria last fall. This fall he plans to return to the Big Apple.

"If you really enjoy living in a big city, New York is the place to be," said Scott, a 38-year-old bachelor who returns to New York just about every weekend.

Other Time-Life employees complained of having to adjust to what one called "the pre-Broadway schlock" at the Kennedy Center, the "uncivilized" dependence on cars, "the homogeneous" nature of Alexandria and the lack of "a vast reservoir of cultural activities."

But not all Time-Life employees are dissatisfied with the Washington area. Marilyn Murphy, a 25-year-old researcher and native of Manhattan who now lives in an Alexandria condominium, siad, "I have a nice garden, a swimming pool and tennis courts. I don't know when I've ever gone swimming before - maybe when I was small."