One minute after midnight this morning, Washington National and Dulles International airports were transferred from federal to local control, bringing an end to decades of legislative debate and making it possible, air travelers hope, for real improvements to be made.

For passengers, the transfer is supposed to mean the construction of new terminals, runways, roadways, baggage claim areas, parking lots and other improvements at aging National and overburdened Dulles.

For the Reagan administration, the transfer represents a legislative victory that continues to surprise the skeptics who said it couldn't be done.

For the Washington area, the chance to control more of its prime assets represents a new degree of local autonomy and economic power.

"It's home rule for the airports," Rep. Frank R. Wolf (R-Va.) said last week. "These airports have been in our area for years and local people have had no say in how they are operated . . . . Now they'll be run by a body that truly represents the views of the people in this area."

Until this morning, National and Dulles were the only major commercial airports in the country owned and operated by the federal government. Now they are leased to and run by the Metropolitan Washington Airports Authority, a powerful new regional body that seems certain to become a major player in the local economy.

The authority will run two enterprises that generated $64.8 million in revenue and $20 million in profits last year. If it were a publicly held company, it would rank in the top 50 in the Washington area.

To renovate the airports, the authority is expected to grant $700 million in design, consulting and construction contracts during at least the next five years. The board's composition -- five members from Virginia, three from the District of Columbia, two from Maryland and one appointed by the president -- will ensure that those contracts are sprinkled across the area and not sucked up wholly by Virginia firms, one board member said.

The authority has the power to generate its own money because it can issue and guarantee its own bonds to finance public works. It is expected to raise as much as $1 billion through bonds over the next five years.

Despite the optimistic pronouncements that have accompanied the transfer, supporters and opponents alike see some clouds on the horizon:A political compromise that eased the passage of transfer legislation resulted in a congressional review board with veto power over the airport board's major actions, and there is the possibility of a legal challenge to the constitutionality of the review board. The airlines serving National and Dulles are clamoring for improvements but don't want to have to pay too much for them. The airports' neighbors are already turning up the volume on their complaints about airplane noise, one of the major burdens the Department of Transportation has been trying to unload on a local body for years.

"I don't expect it to be a bed of roses, but I think we are pretty well on track," said A. Linwood Holton Jr., chairman of the airports board and a principal architect of the transfer.

The United States first attempted to get out of the local airport business in 1949, when the Hoover Commission report on the federal government and its organization recommended incorporating National as a business.

There have been sporadic attempts since then. The Eisenhower, Kennedy and Johnson administrations backed transfer legislation. The Nixon administration proposed turning both airports over to Metro, which was then struggling with Congress to get its subway construction program financed.

The story of how the Reagan administration succeeded where others had failed is one of lobbying, arguing, cajoling, wheeling and dealing, primarily by Transportation Secretary Elizabeth Hanford Dole, the players involved agree.

Dole made the transfer one of her two top priorities (the other was to sell Conrail) and worked furiously for two years to build the coalition of airlines, local businesses, local officials and votes needed to pry the airports from Congress' grasp.

She had the "persistence of a bulldog," said Carrington Williams, an authority board member and chairman of the Washington-Dulles Task Force, a private group that promotes the airport.

The administration's victory also reflects good timing: Dole and her allies pushed for the transfer at a time when the need for improvements and Congress' unwillingness to pay for them were equally obvious.

Airline deregulation and local economic growth have fueled explosive increases in Washington air traffic, particularly at Dulles, which can handle growth with three huge runways and acres of concrete on which to park airplanes. The terminal building, however, has been inadequate to meet the crush of more passengers. In 1986, there were more than three times as many passengers as in 1981, Dulles is now the fastest-growing airport in the nation.

National's traffic has remained fairly stable in recent years, primarily because of the constraints of antinoise regulations and runway length. There is only one main runway and it is relatively short for jet traffic. The terminal itself is still suited only for the passenger counts anticipated when it opened in 1941.

Meanwhile, rising pressure to cut federal spending prevented Congress from appropriating the money needed to relieve clogged baggage carousels, packed parking lots and congested roadways.

The Catch-22 of federal airport budgeting is that, even though they can be offset by revenue, expenditures must be included in the total federal budget, thus increasing that politically sensitive number.

The result was the continued existence of a National Airport that Carter administration Transportation Secretary Neil Goldschmidt once called "a dump."

Nonetheless, Congress balked at ceding control and getting the airports off the federal budget. Some members were opposed to the Reagan administration's campaign to divest government assets. Others worried about losing their preferential parking spaces at both airports. Members of the Maryland delegation vigorously protested any "giveaway" that, they claimed, could leave Baltimore-Washington International Airport at a competitive disadvantage.

Some Virginians demanded a majority on any board set up to govern National and Dulles, because both are in Virginia. District negotiators wanted equal representation.

The inevitable result was deal-cutting.

First, the board's size and makeup were decided. Then the Maryland delegation dropped its opposition after Dole guaranteed $72 million to BWI for runway and other improvements.

Sen. Strom Thurmond (R-S.C.) became a supporter after winning road money for his state, according to sources familiar with the negotiations.

Rep. Jim Wright (D-Tex.), then the House majority leader and now its speaker, insisted that the "perimeter rule" limiting nonstop flights at National to 1,000 miles be extended to 1,250. That additional 250 miles permitted a nonstop from National to Dallas/Fort Worth Airport, next door to Wright's district, and a hub airport for one of Wright's major constituents, American Airlines.

The final compromise was the creation of the congressional review board, which provided the assurance that if local control became too noxious, Congress could reassert its authority.

When the transfer took place this morning, the Federal Aviation Administration's 715 employes at National and Dulles were technically fired. Ninety-three percent of them were immediately rehired by the airports authority. The other 7 percent chose to retire or take other jobs.

The airport authority's directors have years of experience in federal, state and local government. In addition to Holton, a former governor of Virginia, the board includes a former member of Congress, a former undersecretary of the treasury, a former member of the Virginia House of Delegates, a former D.C. Council member and a former D.C. city administrator. Another former U.S. representative, Jack Edwards (R-Ala.), awaits Senate confirmation as President Reagan's appointee. The group also reflects experience in law, commercial banking, management consulting, and transportation consulting.

"Here is a chance to demonstrate that a regional governmental unit can be successful . . . can make a contribution to the solution of problems that are really regional," Holton said, mentioning traffic, water and waste disposal as other such issues. "But I don't want people to think the airport authority is trying to be a regional government."

Despite Maryland's initial opposition to the transfer, former representative Michael D. Barnes (D-Md.), now an authority board member, envisions the day "down the road" when the authority also may run BWI. "The region is growing together, becoming an economic unit. These airports should all boom in coming years as this region and its economy boom," he said.