Three months ago, Fairfax County and Fairfax City were denouncing each other. "Just who do they think they are? What do they think they're doing?" snapped one county official in February.

yesterday, county Supervisor Alan H. Magazine (D-Mason) spoke of "a new era of cooperation and conciliation" between the county and the city. Supervisor John P. Shacochis (R-Dranesville) said the city-county relationship now is "a breath of fresh air."

The "new era" and "fresh air" are being discussed in the midst of resumed negotiations over a contract for the county to operate city schools. Back in December, contract negotiations broke down when the county asked for more money to continue running the schools and the city responded by planning for its own school system.

The election earlier this month of a new mayor and a slate of City Council members pledged to keep the county operating city schools brought about the new contract negotiations that began last Saturday and will continue tonight.

The city now pays the county about $7.7 million to operate six schools serving 4,800 students. In December, the county asked the city to pay an additional $1 million for operating the schools.

City and county negotiators refused to talk about specific disagreements over school costs, saying only that progress is being made and that the animosity of earlier talks now is gone.

Fairfax City mayor-elect Frederick W. Silverthorne agreed there is a "new attitude. We don't expect the county to subsidize city services and the county understand we are not going to subsidize it."

The negotiations probably will be worked out by July 1, according to Magazine, the county's chief negotiator. Ironically, on that date a city-commisioned $50,000 study of the cost of a separate school system for Fairfax City will also be made public.