When Fairfax County Board Chairman John F. Herrity speaks, George T. Snyder Jr. listens. Then he feels free to disagree.

Snyder is mayor of the City of Fairfax (pop. 20,400), a politically independent jurisdiction located in the heart of Fairfax County that serves as the county's seat of government.

This week, Herrity and his colleagues on the county Board of Supervisors gave priority status to finding a private developer to build a new county government center west of Fairfax City on a 183-acre, county-owned site in the Fair Oaks area.

Herrity, who has tried in vain to persuade Fairfax City to widen key road segments and ease traffic near the current county government center, warned that the city's economy would suffer if the county pulled out of its rented office space in Fairfax City. One-third of the city's office space is leased to the county, according to Herrity.

Not so, said Snyder, whose 6.2 square mile city is in the midst of an unprecedented office building boom. He rejected Herrity's figures and said less than a tenth of the city's office space is leased to the county. Figures supplied by city officials appear to support him.

"I don't think there'd be any effect" if the county pulled out, Snyder said in an interview yesterday. "The city is not dependent on the county for its survival."

Herrity said yesterday that his assessment of the county's share of the city's leased office space "was just a guess."

Snyder said the county's rental space in about two dozen city office buildings would be filled quickly if the county departed.

"We have prime real estate and it's going to be filled," Snyder said. "If the county doesn't rent the offices , somebody else will."

The county, whose bureaucracy has outgrown its 12-story Massey Building, spends about $5 million a year to rent office space for more than 1,600 employes in Fairfax City. Several of the city's largest office buildings house county agencies.

County officials say more than 10 large developers already have expressed interest in a joint venture in which a developer would build a new government complex in exchange for valuable county-owned land south of the intersection of I-66 and Rte. 50.

Fairfax City, like the surrounding county, is in the midst of a surge in the construction of office buildings. More office space is currently under construction in Fairfax City than existed there a decade ago. City officials say that vacancy rates are low and that most offices find tenants before they open.

Many of the offices near the county government complex are filled with lawyers and engineers who regularly do business with the county. But in other parts of the city, office tenants have little to do with the county, city officials say.

For years, Herrity opposed building a new county government center west of Fairfax City, charging that supporters of the project had an "edifice complex." Instead, Herrity wanted to build new county offices on the existing site in Fairfax City, a plan that would snarl the already heavy traffic on Rte. 123 through the city.

When Herrity asked city officials to widen and straighten segments of the road near the county government complex, city officials declined, citing the small-town charm of the road's twists and turns.

That was when Herrity decided to back the joint venture to develop a new government center and voiced his concerns over the office rental market in Fairfax City.

"If somebody told me that a third of the business was going to leave Fairfax County," he said, "I'd be pretty upset."

"I'm not overly concerned," countered Snyder. "We will remain a healthy and viable city."