South Carolina Republicans chose a three-term congressman Tuesday to challenge Democratic Sen. Ernest ``Fritz'' Hollings, while a former congresswoman from Arkansas appeared headed for the Democratic nomination for the state's open U.S. Senate seat.

North Dakota Republicans also picked a challenger to a Democratic senator, Byron Dorgan, while in Maine, the two major parties held primaries to see who will oppose popular independent Gov. Angus King. Virginia offered just one contested congressional race, for the GOP nomination to challenge Democratic Rep. Jim Moran.

When Arkansas held its primary three weeks ago, neither former Rep. Rep. Blanche Lincoln nor Attorney General Winston Bryant won a majority vote. That meant Tuesday's runoff was needed to decide the Democratic nominee for Senate.

The winner will face state Sen. Fay Boozman, a 51-year-old religious conservative who hopes to become only the second Republican ever elected to the Senate from Arkansas. The first was Tim Hutchinson, who defeated Bryant two years ago.

Lincoln _ who quit Congress in 1996 after having twins _ was the top vote-getter in the May 19 primary for the seat that is open because Democrat Dale Bumpers is retiring after 24 years.

With almost one in five counted, Lincoln led with 28,416 votes, or 63 percent of the vote, to Bryant's 16,493 votes, or 37 percent.

Lincoln, 37, is looking to emulate the first woman elected to the U.S. Senate, Hattie Caraway, who in 1932 defeated a crowded field of men in Arkansas' Democratic primary, then easily beat the Republican candidate.

``If she wins the runoff, this has the potential of being the most interesting Senate race in the country,'' said Gary Nordlinger, a Democratic Party consultant in Washington. ``You've got essentially the old-school conservative Republican against the young energetic mother of twins.''

In South Carolina, Rep. Bob Inglis easily defeated Stephen Brown, a former GOP county chairman, for the Republican Senate nomination and the right to take on Hollings, who is seeking his sixth full term.

Inglis had 91,129 votes, or 74 percent of the vote, to Brown's 27,593 votes, or 22 percent, with 81 percent of precincts reporting.

Although Hollings is unopposed for his party's nomination, the 76-year-old incumbent has spent more than a half-million dollars on ads. A recent poll by Mason-Dixon showed a Hollings-Inglis race as too close to call.

Political analysts said a lopsided primary victory for Inglis, 38, could make him a greater threat to Hollings.

``A large victory gives him momentum; a weak or marginal victory leads to questions of whether he should be in the race at all,'' said College of Charleston political scientist Bill Moore.

South Carolina Gov. David Beasley, 41, seeking his second term, easily won the Republican nomination, getting more than 70 percent of the vote. The Democratic candidate is former state legislator Jim Hodges.

In Maine, the Democrats running for governor were lawyer Thomas Connolly and race track owner Joseph Ricci, with state Rep. William Lemke a write-in candidate. The Republican field consisted of former Rep. James Longley Jr., state Rep. Henry Joy and former state Education Commissioner Leo Martin.

Longley's father was governor as an independent for one term in the 1970s. Independents form the largest bloc of voters in the state.

With 2 percent of precincts reporting, Longley led the Republican race with 61 percent of the vote; on the Democratic side, Connolly led with 84 percent.

Dorgan had no primary opposition in North Dakota and is heavily favored for re-election to a second term. Former Fargo state senator Donna Nalewaja (pronounced nal-uh-WHY-uh) was the GOP favorite; with just 1 percent of precincts reporting, Nalewaja had 65 percent of the vote.

In Virginia's 8th District in suburban Washington, Demaris Miller, a former nurse and teacher, won the GOP primary, beating Chuck Carlton, who owns a temporary employment service. Mrs. Miller got 5,195 votes, or 55 percent of the vote, while Carlton had 4,206 votes, or 45 percent.

Mrs. Miller's husband, Jim Miller, was budget director for President Reagan and lost two GOP Senate primaries, including a bruising 1996 contest against Sen. John Warner.