Relations between Fairfax City and surrounding Fairfax County, never very amicable, arelikely to deteriorate further as a result of the county Board of Supervisors' decision to seek renegotiattions of all service contracts with the city.

In a resolution adopted unanimously at its Monday meeting, the supervisors said "county taxpayers are subsidizing city services . . . in amounts which, over time, may be measured in millions of dollars."

The county supplies the independent city with about $8.5 million worth of services annually.Those services include school operations (the biggest item, costing more than $7 million), sewage treatment, solid waste disposal and fire protection.

Fairfax City Mayor Nathaniel F. Young, in a cool response to the county's action, said, "I'm not particularly interested in renegotiating everything. It's just a little bit innacurate to say the county is being taken."

The city's main interest is in resolving a dispute it has with the county over the contract covering the annual tuition payment to the county school system. The city contends the county overcharged it $1,131,501 during 1972-1976. The county, on the other hand, claims the city was undercharged $542,000 between 1965, when Fairfax City became independent, and 1972.

Fairfax City school board chairman George A. Hamill said the county's decision to seek renegotiation of all service contracts "in one big ball of wax" will make it more difficult to resolve the dispute over tuition charges.

The supervisors' resolution indicates that board members want to deal with all questions about services together, contrary to the city's wishes. The county school board apparently feels the same way. On Monday the school board revealed that in a closed session on Saturday it voted to seek renegotiation of the tuition contract "and requests the . . . Board of Supervisors to join . . . in opening such negotiations . . ."

The best relationship that the city and county have been able to attain has been a truce between periods of open warfare.

While the county surrounds it entirely and provides it with many services, Fairfax City is an independent entity.

Occassionally, assertions of this independence have irked the supervisors. For example, Fairfax City, all by itself, was able last year to kill the regional gasoline sales tax. The county had been hoping on revenues from the tax to balance its budget.

While county officials denounced the veto as a selfish move, city officials were saying the county had only itself to blame. Mayor Young said city officials had been told the county to push for enabling legislation that would permit each jurisdiction in Northern Virginia to impose or not impose the tax. Instead, Young said, county leaders accepted legislation that made the levy dependent on approaval by all jurisdictions.

The present mood of the supervisors was indicated by comments some of them made prior to adoption of Monday's resulution. Martha V. Pennino (D-Centreville), for example, said "I think it's terribly unfortunate the city didn't use the contracts committee over the last year resolve differences with the county . . ." Mrs. Pennino, who is chairman of that committee, said that instead they city resorted to the courts and to the press "to get sympathy."

But Mayor Young, in an interview, said: "When is the last time Mrs. Pennino called a meeting of the committee? She hasn't called any meetings."

The county's decision to renegotiate all contracts could, Young said, leave the county's governmental complex in the Massey Building and 12 square miles of the county without close-in fire protection.

The mayor said the decision apparently undoes what he described as a verbal understanding on the city's takeover of the fire station, presently operated by the county, one block south of the Massey Building. Young said under the agreement, the city agreed to continue fire protection of 12 square miles of the county in exchange for county reimbursements involving training and communications equipment.

If there is no agreement by April 19, a Fairfax City spokesman said, "we will provide fire protection for the city and the country can provide for the county."

Mayor Young, who supported the gasoline sales tax sought by the county last year and generally has declined to engage in public skirmishes with leaders of the bigger jurisdictions, said: "They can't stand to be wrong. Theythink they're omnipotent."