Republicans showed substantial strength in local Northern Virginia elections yesterday, narrowing the Democratic majority to one vote on the Fairfax County Board of Supervisors and retaining their hold on the Arlington County Board.

The GOP also picked up two seats on the seven-member Prince William County governing body and one seat in Loudoun County, although Democrats maintained majority control of both.

In Fairfax, Republican newcomer Thomas M. Davis III crushed Democrat Betsy W. Hinkle for a board seat controlled by Democrats for nearly a decade. Davis' victory means the GOP, which before 1976 had only oneseat on the nine-member board, now control four seats, just one shy of a majority.

The six Fairfax incumbents -- four Democrats and two Republicans -- all retained their seats.

Democrat James M. Scott won by the narrowest margin beating Republican challenger Gwendalyn F. Cody by six percentage points, 53 to 47.

Democratic incumbents Martha V. Pennino, Audrey C. Moore and Joseph Alexander all rolled to relatively easy victories as did GOP Board Chairman John F. Herrity. Republican Supervisor Maria B. Travesky of Springfield also won by a substantial margin in a bitter three-way race against Democrat Carl E. J. Ericson and Joseph D. Ragan Jr., a maverick Republican who ran as an independent.

Democrat Sandra L. Duckworth defeated Republican T. Farrell Egge for the Mount Vernon seat vacated by a Democrat. The GOP's Nancy K. Falck succeeded a fellow Republican in Dranesville by rolling up a 3-to-2 margin over Democrat Maya A. Huber.

In the Arlington County Board race, incumbent Republicans Dorothy T. Grotos and Walter Frankland Jr. defeated Democratic-backed challengers Mary Margaret Whipple and Charles Rinker for new three-year terms.

Their reelection means that the Republicans will retain majority control of the board, which for most of the last quarter-century had been controlled by a liberal Democratic coalition.

"It has been a rough campaign," Grotos said last night. "I'm just glad the citizens of Arlington realized what we were doing. We're going to really upgrade Arlington and make a lot of improvements."

Frankland, who is expected to become chairman of the County Board next year, told a cheering crowd of supporters at a South Arlington hotel that the Republican board would "bring academic excellence to the school board."

In Loudoun County, final unofficial returns showed Republican Andrew Bird defeating Democratic incumbent Shannon H. Geddie in Sterling. Seven other incumbents -- six Democrats and one Republican -- were reelected, leaving the board with a 6-to-2 Democratic majority.

In Prince William County, Democrat G. Richard Pfitzner defeated independent incumbent James Byrd, while Republican Donald E. Kidwell beat Democratic Supervisor Alice E. Humphries. Democrats retained four of the seven board seats, while Republicans picked up two seats and independents dropped from three seats to one.

Indications were that voter turnout in all four localities was moderate -- between 40 and 50 percent.

In Fairfax, GOP candidate Davis won a low-key campaign emphasizing neighborhood issues despite that fact that outgoing Supervisor Alan H. Magazine supported Davis' opponent Hinkle.

Another key race was the acrimonious contest between Travesky, Ericson and Ragan in the sprawling Springfield District, where most of the county's developable land and drinking water resources are located.

Travesky found herself under a two-sided attack, with Ericson accusing her of being too conservative and working "hand-in-hand" with developers to despoil the district, the country's largest. At the same time, Ragan tagged her as too liberal for supporting public housing and pay raises for county officials.

The Providence District race between incumbent Scott and Cody was also considered close. Scott -- the last surviving member of the liberal Democratic coalition that dominated the board in the early 1970s -- was attacked by his conservative Republican opponent as being too liberal, even "socialistic," and free spending.

Considered less vulnerable were incumbent Democrats Moore, Pennino and Alexander, all of whom projected more conservative images than Scott. Moore, a critic of development in the fast-growing county and a gadfly on the board, appeared to have the largest following and most recognizable name among board members.

The GOP's recognizable local candidate was incumbent Board Chairman Herrity, who last year had failed in a bid for a congressional seat. A conservative Republican with a flair for publicity, Herrity was generally thought to have outspent and out-talked his Democratic opponent, Vivian Watts.

Herrity kept his reputation for dramatics intact yesterday morning by jogging to the polls in the predawn darkness.

The GOP had hoped to capitalize on the retirement of Democratic incumbents in Mason and Mount Vernon districts and to retain the Dranesville seat being vacated by a Republican. That campaign between Republican Falck and Democrat Huber was one of the most competitive and generated the most campaign gifts of any single-district race.

Support for Metro was the key issue in the Arlington County Board race. Democratic-backed challengers Whipple and Rinker attacked Grotos' and Frankland's voting records on Metro and accused the Republican-backed incumbents of trying to stymie the system until popular support for Metro made that stance a political liability.

Frankland and Grotos insisted they supported Metro -- Grotos said recently that the system was so popular "even the pope couldn't stop it" -- and said their votes since their election in 1975 reflected concern over financing the system.

The fifth candidate in the race, Libertarian-backed Michael M. Maddox, called Metro a "tax monster" and opposed completing it.