For years, every time the question of interstate banking was mentioned, Washington-area bankers recoiled, fearful that they would be swept up by giant New York banks.

So earlier this year when Virginia and the District opened their borders to interstate banking, they limited it to banks in other states in the Southeast quadrant of the nation and excluded the big, so-called "money-center" banks.

But while they boarded up the north door of the henhouse against the New York wolves, they opened the southern gate to three of the most agressive bank companies in the nation -- the North Carolina banking giants, financially stronger than most money-center bankers and used to rough-and-tumble statewide competition with each other.

In the few months that regional interstate banking has been a reality in the Southeast, the three North Carolina banks have gone on an acquisition spree, buying institutions in Georgia, South Carolina and Florida.

Since 1982, before the onset of regional banking last summer, NCNB had been assembling a Florida network using a trust company it bought there in 1972.

The aim of all three banks, their chief executives said, is to build big, regional bank companies that are firmly based in the Southeast.

Soon, probably in 1987, they will be seeking acquisitions in Virginia, Maryland and, perhaps, the District, the executives of all three banks said.

"Like Caesar having conquered all of Gaul, we look northward," said Hugh McColl, chairman and chief executive of NCNB Corp.

But McColl and Edward Crutchfield Jr., chairman of First Union Corp., said that a foray into Virginia, whose affluent Washington suburbs are the most attractive area to conquer, is not imminent.

For the next year or so, the two Charlotte banks, whose headquarters are within two blocks of one another, will concentrate on assimilating the banking empires they have already begun.

Just Friday, NCNB received Federal Reserve Board approval to buy banks in Florida, Atlanta and South Carolina.

On the same day, First Union completed its merger with a $3 billion North Carolina bank, Northwestern Financial Corp., and two weeks ago swallowed the $3.8 billion Atlantic Bancorp of Jacksonville.

First Union has four more mergers in process -- two more in Florida and one each in South Carolina and Georgia.

"We accomplished our five-year plan in six months," said First Union's Crutchfield. "We don't have another one. We've got to create one."

As a result of their lightning-quick interstate acquisitions this year, the North Carolina banks have climbed almost overnight into the ranks of the nation's giants.

A year ago, only one North Carolina bank company, NCNB, was counted among the top 25 banks in the nation in asset size, and it was at the bottom of the list. When all the mergers announced in the last few months are finished, all three major North Carolina bank companies -- NCNB, First Union Corp. and Wachovia Corp. -- will be among the largest 20 banks in the country.

When the mergers are finished, NCNB will have assets of about $21.5 billion, First Union will control assets of $17.1 billion and Wachovia -- which will be called First Wachovia after it merges with First Atlanta Corp. this month -- will become a $16.7-billion institution. Each is Bigger Than D.C.'s Total

Any one of these three banks have more assets than all of the banks in the District combined.

Atlanta, long considered the banking capital of the southeastern United States, is rapidly being eclipsed by Charlotte, the home of NCNB and First Union, and Winston-Salem, where Wachovia Corp. is headquartered.

Both NCNB and First Union have adopted remarkably similar expansion strategies.

In Florida, the fastest-growing market in the region, the two banks have purchased, or are in the process of acquiring, large banking networks.

In South Carolina, which is visible from the top floors of each of their headquarters buildings, they also are putting together big bank networks.

South Carolina, Crutchfield and McColl said, is a logical extension of their North Carolina business.

In Atlanta, however, they are purchasing small toehold banks that will permit them to develop a bigger business lending presence without competing head-to-head with big Atlanta banks for consumer deposits.

For NCNB, however, the Atlanta strategy is a fallback. Initially, NCNB sought to buy the $7.4 billion First Atlanta Corp.

But First Atlanta rebuffed a more lucrative NCNB offer and instead merged with Wachovia. Wachovia's Only Out-of-State Buy

The Atlanta acquisition is Wachovia's only out-of-state purchase.

Both NCNB and First Union make no bones about being the headquarters institution.

Wachovia Chairman John Medlin said that First Atlanta and Wachovia will retain their separate identities after they become subsidiaries of the new First Wachovia Corp.

Other North Carolina bankers said privately that the arrangement will not work long. The bigger and stronger Wachovia will dominate the partnership.

First Wachovia will soon discover, they said, that the company cannot be run effectively from two headquarters.

But even as the giant North Carolina banks take time to digest their new acquisitions, they are also looking to the future. And the future includes Northern Virginia.

"We will be in Virginia," said First Union's Crutchfield.

Both Crutchfield and McColl plan to be in Tennessee and Maryland as well, but said that their plans for those two states now envision toehold operations, similar to their Atlanta strategy, in Baltimore and Nashville.

Medlin of Wachovia said his bank is interested in expanding to Tennessee, South Carolina, Florida and Virginia.

To tap the Virginia market, the North Carolina banks want a large number of offices in the Virginia suburbs of Washington, where affluent retail customers and their deposits are as abundant as growing companies that need bank services. Unequal Laws Impede Acquisitions

But the crazy-quilt of state laws that govern regional bank merger pacts may make it difficult for the North Carolina institutions to acquire their Northern Virginia operations the easiest way -- by purchasing a big bank with a string of suburban offices.

While Virginia and the District of Columbia have passed laws permitting any banks in the Southeast region to buy banks in Virginia or the District, providing the states in which the banks are headquartered permit District and Virginia banks the same privilege.

Meanwhile, Maryland has relaxed its out-of-state barriers only to bordering states. No Maryland Mergers Until 1987

Not until mid-1987 will North Carolina banks be permitted to merge with Maryland institutions.

"That's the reason Virginia banks are buying Maryland banks first," said Crutchfield.

"It protects them against a North Carolina acquisition. We can't buy a Virginia bank that owns a Maryland bank."

By 1987, the Virginia banks may be too big to be swallowed, even by the large, aggressive North Carolina banks.

"It's a risk you have to take," said NCNB's McColl. "I can't bite off more than I can chew."

Crutchfield said that First Union will if necessary assemble a Northern Virginia network by purchasing a string of smaller banks -- even though that is a more cumbersome procedure than acquiring an already intact network.

But North Carolina banks are used to that approach. The three large North Carolina banks put their statewide networks together through a series of mergers with smaller banks. N.C. Now Has Only 60 Banks

In 1960, there were about 250 banks in North Carolina. Today there are about 60.

"I was raised on mergers," said Crutchfield. "Since 1957 this bank has seen 45 mergers. At one time you couldn't merge but once every 90 days. We used to have them lined up like airplanes at La Guardia," he said.

"Every 90 days we'd do another one," he added.

"One of the advantages of mergers is that it spreads the costs of technological investments," said John Medlin Jr., chairman of Wachovia.

"In the last 10 years we have tripled our assets, quadrupled our earnings but increased our employes by only 26 percent," Medlin said.

He said the bank increased its spending on research and development fourfold during the same period.

A smaller bank could not justify that level of increase in research spending, but the spending is necessary to remain competitive, Medlin said.

But North Carolina banks have about run out of room to grow in the state.

The three big banks account for more than 70 percent of North Carolina's banking assets.

The three North Carolina institutions already dominate the Southeast region and expect to continue to do so in the future.

Because North Carolina has well-developed and broad-based industries, from tobacco to furniture to the high companies in Raleigh-Durham, the big North Carolina banks have long had to offer a menu of sophisticated banking services that most regional banks have not, according to one bank analyst.

"That means they won't have as much to learn as some banks," he said.

"We're also well-managed and strong," said Crutchfield.

Crutchfield attributed that to the intense competition among all three.

"We probably wouldn't be so good if they [Wachovia and NCNB] hadn't been so good," he said.

But the chief executives of all three North Carolina institutions said that giant banks they are assembling will never lose their "regional" characteristics. 'We Understand . . . the Southeast'

"We understand how business is done in the Southeast," said Wachovia's Medlin.

The banks have relationships with companies all over the country, but the bulk of their lending business is with consumers and middle-sized businesses in their local markets.

The North Carolina banks plan to continue to lend mainly to middle-sized companies, those with sales from $5 million to $500 million, and to rely on consumer and small business deposits rather than tapping national money markets for the bulk of their funds.

But wherever they go, the North Carolina banks feel they will be competing with each other -- as they have been for the last two decades when the wave of consolidations and mergers began in the state.