Four Republican moderates swept to victories yesterday in Northern Virginia primary elections for November's state legislative races, while Fairfax County Supervisor Nancy K. Falck survived a strong challenge from a fellow Republican in the Dranesville District.

The primaries appeared to signal another victory for Republican moderates in Fairfax, who have clashed with conservatives bitterly and often in recent years. The infighting, party officials acknowledge, has only helped Democrats.

In a hotly contested and expensive contest, Bobbie Kilberg, a lawyer and former White House associate counsel, scored a resounding victory against conservative civic activist Joyce Sutcliffe in the GOP primary in the 32nd state Senate District, which includes northern Fairfax and Arlington counties and Falls Church. With all but one precinct counted, Kilberg had a nearly 2-to-1 lead against Sutcliffe.

The Kilberg-Sutcliffe race was one of 14 Northern Virginia primaries for party nominations for the General Assembly and for supervisor seats in Fairfax, Prince William and Loudoun counties.

The general elections will be held Nov. 3.

In other Republican primaries for the state legislature, Jane Woods, a Fairfax County teacher, easily defeated Robert W. Beers, a conservative lawyer, in the 37th House of Delegates District of central Fairfax County. Woods had 62 percent of the vote; Beers had 38 percent.

In a result that surprised Republican Party regulars, A. Strode Brent Jr., a lawyer and political newcomer, edged former state delegate Gwendalyn F. Cody, a conservative, by only 10 votes out of nearly 2,700 cast in unofficial returns in the 38th House District of eastern Fairfax.

C. Ronald Smith, 39, a lawyer, beat former county School Board member Gerald Fill, 48, in the 36th state Senate District in southern Fairfax, 54 percent to 46 percent. Fill was considered by some Republicans to be the more conservative candidate.

While the moderate forces managed to throw out a conservative Republican Party chairman in Fairfax County two years ago, the conservatives have continued to field candidates such as those in yesterday's legislative primaries -- a sign that the rift has not closed.

"I think this is what you find throughout the country, that the moderates are the ones who get the votes," said county GOP Chairman James M. Swinson, a moderate. "In this area, they also make the best candidates."

Turnout yesterday was low, in keeping with past voting patterns for off-year primaries, in which there are no national or statewide races. While Northern Virginia voters tend not to vote along party lines, the primaries are an occasion for the party faithful to make their mark at the polls.

In a closely watched primary for local office, in Fairfax County's Dranesville District, county supervisor Falck, an eight-year incumbent, defeated Lloyd L. Thoburn, a 25-year-old conservative who is administrator of a Christian school. Falck had 53 percent to Thoburn's 47 percent.

Falck's margin of victory was apparently narrower than she expected, perhaps signaling a tough reelection battle this fall. Thoburn's father Robert, a former state delegate, filed yesterday as an independent in the fall general election.

There were some reports that Democrats crossed over to vote against Falck in the Republican primary, boosting Lloyd Thoburn's total.

In Virginia, voters do not register by party and can legally vote in any primary in a district in which they reside.

Joining Falck, 57, and Robert Thoburn in the fall race in Dranesville will be Democratic civic activist Lilla D. Richards, 48, who received 93 percent of the vote in her primary race against Franklin S. Holland Jr., 31, assistant manager in a vacuum cleaner and sewing machine shop.

In Prince William County, Supervisor Edwin C. King, 57, soundly defeated former state delegate Floyd C. Bagley, 65, in a Democratic primary for county board in the Dumfries District. With no Republican in the race, King, who received 56 percent of the Democratic vote, is considered a heavy favorite over independent Norma Pandazides in the general election.

Kilberg will face Democratic state Sen. Clive L. DuVal 2d, dean of the Northern Virginia delegation to the state legislature, on Nov. 3.

Woods, who capitalized on a strong base of support in Fairfax City in her primary contest, will be running in the only Northern Virginia legislative district without an incumbent seeking reelection. She will face Democratic lawyer Jeffrey J. Fairfield, 36, who nearly won the seat two years ago.

Brent will face the woman who unseated Cody two years ago, Democratic state Del. Leslie L. Byrne.

Smith will face Democratic state Sen. Joseph V. Gartlan Jr., 61. Officials of the two major parties say it is highly unlikely that Gartlan, a lawyer who is one of the most respected members of the General Assembly, can be dislodged this year.

Virtually every primary in Northern Virginia was marked by incumbents and challengers who pledged to devote their attention to the region's mounting transportation problems. Aside from that rhetorical unanimity, few themes connected the contests.

All four of the region's state legislative primaries were Republican contests. Indeed, they were the only Republican primaries for the General Assembly in the state yesterday.

In the 32nd state Senate District, Kilberg and Sutcliffe clashed over social issues and waged one of the most expensive primary battles for the state Senate that Virginia has seen. Sutcliffe, 47, said she would view legislation with an eye to "how it impacts upon the family." And she charged that Kilberg, 42, whose long list of donors includes nationally known Republicans and out-of-state lawyers and developers, is a feminist and a liberal who would represent "out-of-state interests."

Kilberg spent nearly $50,000 in the primary, and Sutcliffe spent about $10,000.

Kilberg, who describes herself as a moderate, emphasized her "electability" in a district that, while heavily Republican, has voted for DuVal four consecutive times.

Republican officials reported an undercurrent of anti-Semitism directed at Kilberg, who is Jewish. Sutcliffe acknowledged the existence of the sentiment among a small number of voters but disassociated herself from it.

DuVal, a lawyer who will turn 75 this month, has said he plans to retire after one more term. He is considered the senior statesman of Northern Virginia politicians and is likely to be regarded as the favorite in the general election campaign despite the heavy attention focused on the Kilberg- Sutcliffe match.

The Fill-Smith race took place in the 36th state Senate District, which includes the area of Fairfax County south of Alexandria and parts of Springfield.

In the 37th House of Delegates District, Beers, a 39-year-old lawyer, and Woods, a 40-year-old teacher, vied for the Republican nomination for the only open legislative seat in Northern Virginia. The Republican incumbent, Stephen E. Gordy, 67, is retiring.

In the 38th House District, Cody, 65, was the slight favorite going into the primary, in part because she has served two terms in the House of Delegates. But Brent overcame the odds to win by 10 votes, a margin that he characterized jokingly last night as "a landslide."

Brent raised about $10,000, compared with $15,000 for Cody.

Brent, 45, still faces an uphill battle in the 38th District, where incumbent Byrne, 40, is likely to be regarded as the favorite in the fall elections. A businesswoman in Seven Corners, she received favorable reviews during her first term in the House.

Even Brent acknowledged in a television interview that Byrne's first term had been somewhat successful -- an unusual admission for a challenger to make about an incumbent.

There were two downstate Democratic primaries. In far Southwest Virginia, Del. James W. Robinson of Pound failed to win his party's nomination to a fourth term, losing to 9th Congressional District Chairman Jack Kennedy, who got 61 percent of the vote.

In Norfolk, Jerrauld C. Jones, an attorney supported by the local Rainbow Coalition, narrowly defeated Robert R. Ambrose, a teacher, 51 to 49 percent, for the Democratic nomination in Norfolk's 89th House District. The incumbent, Yvonne B. Miller, also a Democrat, is vacating her seat to run for the state Senate.