The five-month struggle among Virginia, Maryland and District officials over who should operate National and Dulles airports has reached a virtual deadlock, members of the commission appointed to settle the dispute said yesterday.

The 15-member Holton Commission, appointed by Transportation Secretary Elizabeth Hanford Dole, has reached such an impasse that it is asking D.C. Mayor Marion Barry, Maryland Gov. Harry Hughes and Virginia Gov. Charles S. Robb to settle the dispute for them, sources said. The three are commission members, but have had subordinates serve on the panel.

"We recognize we've come to a stage where we've got a difficult decision to make," said former Virginia Gov. Linwood Holton Jr., the commission chairman. Holton canceled yesterday's meeting of the group, at which members were to announce the plan for transferring authority for the airports from the Federal Aviation Administration to a local authority. "Cathedrals are built one stone at a time," he said. The commission will next meet on Dec. 13.

The delay is only the latest sign of the problems faced by the commission in drawing up a plan to have the federal government divest itself of the airports. The latest squabble centers mostly on how many members each jurisdiction should have on a planned nine-member local airport authority.

Dole has met with both Barry and Rep. Steny Hoyer (D-Md.), and has indicated she is "prepared to meet with everybody if necessary" to reach a compromise, said one commission member. The two governors are talking by telephone with central figures, including Holton, and a meeting between them and Barry is being considered for next week, sources said.

"It became clear as time went on that the senators and congressmen [on the commission] would change their tune if the governors would," a panel member said. "It's all politics."

Holton said that since a consensus will be difficult, he will depart from previous plans by not sending Dole a formal commission recommendation on the composition of an airport authority. Instead, he said he will submit a summary of each commission member's position on the question.

Virginia members, including elected officials in Alexandria and Fairfax and Arlington counties, want Virginians to dominate the airport authority because they bear the brunt of jet noise at the two Virginia airports, and have an interest in the real-estate development around them.

Maryland and District officials say they deserve equal representantion on an airport board. They want each jurisdiction to have three members on the airport board.

But that plan would be hard to swallow for Virginians, since most scenarios state that the authority would be constituted either as a Virginia state agency (with members from all three jurisdictions) or as a joint Virginia-District authority with some Maryland representation. Either way, the Virginia General Assembly would have to approve participation in an airport authority.

"I don't even have to talk to leaders in the Virginia General Assembly to know it isn't going to fly down there unless Virginia is given a majority" on the airport authority, said Fairfax Supervisor Martha V. Pennino, a Holton Commission member. "We're at a stalemate right now, and if Maryland officials don't budge [on the three jurisdictions having three members each], we're going to stay there."

Another problem, frequently mentioned by Virginia officials, is that Maryland members on an airport authority could have a conflict of interest because Dulles is locked in a serious competition for passengers and flights with Baltimore-Washington International Airport, which is owned by the State of Maryland. Marylanders on an airport board would gain confidential information about Dulles' operation and could sabotage Dulles in its battle with BWI, Virginia officials say.

James Truby, Maryland's aviation administrator, yesterday called that allegation a "red herring" and added that Maryland members of a Dulles-National board would act "in a manner consistent with those airports' interest."

As sticky as this dispute seems, one commission member said it is "the easy part" compared with the next step: sending recommendations to Dole, who will send legislation to Congress to transfer the airports.

Congress members and the airlines have prevented repeated attempts in the last 35 years to remove the airports from federal control, and all sides agree that those two groups are still opposed.