RICHMOND, DEC. 3 -- High atop the noble buildings of Capitol Square here, the mighty Virginia state government is challenging an enemy it can discourage but never defeat, a creature that no bureaucrat here or elsewhere will ever regulate effectively.

For weeks now, at least three state agencies have been trying to scare away the droves of pigeons that have descended on Richmond's historic complex of government buildings now that the birds' summertime diet of grains has been plowed under on the farms of Virginia.

So far, the best efforts of the state Bureau of Buildings and Grounds, Department of Agriculture, and Commission of Game and Inland Fisheries have paid off. Numerous pigeons have been captured, then transported out of town or destroyed, according to several official spokesmen.

But if the seasonal battle has been won, the war will surely be lost, these officials conceded today. "We'll never have a shortage of pigeons," acknowledged John R. Tate, an assistant supervisor in the Agriculture Department.

Tate and other grizzled veterans of the annual pigeon wars liken the birds to airborne rats, scavenging pests that soil the rooftops of the Jefferson-designed state Capitol, the governor's mansion and other agency headquarters in downtown Richmond.

"We try to keep some as an attraction for all the tourists and visitors to the Capitol, but they're also a very bad nuisance when they roost on the roofs," said Allan Platt, superintendent of buildings and grounds.

The state's pigeon "containment policy," as Platt put it, is pretty simple. State workers have installed and baited wire traps on some buildings to catch the pigeons and installed a product called Roost No More, which are strips of metal needles, to further discourage the birds from alighting on their perches.

There are some drawbacks, though. For one thing, "Pigeons are very bright," and learn to avoid the traps, Platt said. In addition, the antipigeon campaign has sparked more than a few complaints from bird lovers, Tate said.

The humans might have a secret weapon in the form of a large hawk that frequents Capitol Square to feast on the excess wildlife there. But there again, Mother Nature has fooled the pigeon-fighters.

"The hawk seems to favor ground squirrels," Platt said.