Fairfax Board of Supervisors Chairman Audrey Moore and Thomas M. Davis III (R-Mason) exchanged pleasant conversation as they drove alone in Davis's station wagon Monday to the funeral of a friend.

There was no shouting, no accusations. They even let each other finish their sentences without interrupting. Democrat Moore did not accuse Republican Davis of being a stooge for developers and Davis withheld wisecracks about flip-flops by Moore.

Still, it was not easy. "It would be difficult to get the two of us to sit together for any other occasion," Davis said.

The fierce competition between the two, which has been carried on through name calling and reporter-spinning behind the scenes for months, is heating up as the election year gets underway. The stakes are high, with the winner being able to shape Fairfax County's agenda through the mid-1990s and have a large hand in issues ranging from selection of a new county executive to picking transportation initiatives.

But before Moore can have another four years to make good on her balanced-growth policies, and before Davis has the chance to be the consensus-building chairman, they must knock out festering challenges from within their own parties that stand between them and winning their nominations.

Challenging Moore is Democrat Michael S. Horwatt, a well-connected Fairfax lawyer, whose strength comes from a business community that feels alienated by the current Democratic-controlled board.

For his part, Davis, the boyish Mason District supervisor, has been unable to deliver a knockout blow to former chairman John F. "Jack" Herrity, who has been mounting an energetic effort by contacting businesspeople, developers and party committee people during the last several months.

"We are going to announce," Herrity said last week. "All that has to be decided is the date. You can make that the lead of your story."

But some Republican insiders say Herrity doesn't really have much of a chance, with lots of political "baggage" from his 1987 disaster, in which Moore beat him by a 3-2 ratio, and with only $3,400 in his campaign chest. Davis, who has held a few fund-raisers to add to the $30,000 or so he had left from 1987, claims he will have $100,000 in his war chest by the end of January.

But Herrity, who is looking for respect and credibility, said his effort is going right on schedule, with a major fund-raiser planned for next month. He sent a letter 10 days ago seeking $1,000 and $500 donations to the fund-raiser.

"The campaign is a series of hurdles, and the first hurdle is the nomination," said Tom Herrity, the candidate's son. The Herritys say that a party convention, scheduled for August, gives them an edge over the heavily financed Davis because it will appeal to their strengths: organizational expertise and grass-roots politics.

"Just like his finances, just like his canceled fund-raisers, they're trying to put the best face on it," Davis said of the nominating process. "We will know May 18," when delegates file to participate in the convention and name their preference. "If he outfiles me significantly, I will get out of the race."

Meanwhile, Herrity is eating into Davis's money and efforts, which could be held in reserve for the push against Moore. While Davis ate breakfast at the exclusive Tower Club in Tysons Corner last week with developer J. Bahman Batmanghelidj, Herrity sat at the next table with Tom Grubisich, part-owner of The Connection newspapers. Davis had a date with Grubisich within 24 hours. Davis also scanned Herrity's contribution list, which Herrity filed last week, and asked contributors why they gave to the other side.

"I'm not after their money," said Davis, who is trying to shake the image of a developer's candidate that Moore will seek to lay on him. "I just don't want them giving to Herrity."

Judging from her rhetoric, Moore is seeking to portray the primary and general election as a clash between the forces of light and dark -- between people who are not developers and those who are, or make their money through development.

"I've got three developer-backed candidates against me," said Moore, who refers to Horwatt as "a very nice guy who's being supported by developers . . . . I'm trying to balance transportation and growth."

Horwatt, who accuses Moore of "bolting" from her own programs, such as revenue bonds for the Fairfax parkway, calls that type of talk "insulting and outrageous."

"If you disagree with her, you're accused of being in the pocket of developers, and that's absurd," said Horwatt, who will point to a record of public service. "The underlying assumption is that you're a sellout because you're against Audrey Moore. That's how she has intimidated every public official into a silence about her."

Horwatt's major problem is overcoming Moore's advantage with the core of Democratic Party activists, whose allegiance she has carefully cultivated during the last three years. That core of 400 to 500 people will play the major role in determining the next nominee.

To try to cement her hold on the nomination early, Fairfax Democratic Party Chairman Harris Miller sent a letter to committee members declaring his support for Moore. He also took the unusual step two weeks ago of phoning reporters to proclaim his support.

Miller last week was host of a birthday fund-raiser for Moore at his McLean home that drew 150 to 200 people, according to Moore supporters. Before the money had been counted, the estimates were that she raised between $5,000 and $10,000.

Before she blew out the candles on her birthday cake, Moore looked up and asked everyone to guess what she was wishing for.