Tysons Corner, the thickly developed area of mammoth shopping malls and sprawling office parks that has been called Fairfax County's downtown, has a rural problem: deer.

Office workers at Honeywell Inc., just off the Beltway at 7900 Westpark Dr., yesterday spotted from their window more than a half dozen deer frolicking on an empty lot out back. The lot, now covered by scrub, is part of the site for the huge Tysons II development, for which construction is scheduled to begin soon.

Betsey T. Capraro, a librarian at Honeywell who saw the animals, called Nancy K. Falck, the Republican who represents the Dranesville District on the County Board of Supervisors. Falck brought the matter up at yesterday's board meeting.

"The county has all the doe," smirked Supervisor Thomas M. Davis III (R-Mason).

Board vice chairman Martha V. Pennino (D-Centreville) had more serious concerns. "As soon as this gets out," she said, "everyone with a bow and arrow or a BB gun is going to be out there."

Richard F. Amity, the county's director of animal control, said the deer at Tysons won't be easily removed.

"It's one of those no-win situations," he said. "If we attempt to drive them out, they could run out over heavily traveled roads. If we attempt to shoot them with an immobilizer or tranquilizer, they could die because deer have extremely fragile nervous systems, or else they could die on the road in the two or three minutes before the drug takes effect.

"No matter what we do, we're going to offend somebody," he said.

Amity said the county could be held liable if a deer shot with tranquilizer runs out in front of a vehicle and causes an accident before the drug takes effect. He said the state has large box traps that could be used on deer, but they are unwieldy and not always effective. The board asked Amity to explore the matter further.

Davis concluded: "I think you can accuse us of passing the buck."