Some voters also will decide county and municipal elections, but they won't vote on presidential candidates. The state held its presidential primary in February. That race was won by Democrat Hillary Rodham Clinton and Republican John McCain.
The campaigns for each party's nomination for a U.S. Senate seat have proven contentious.
Democratic incumbent Frank Lautenberg is being challenged by U.S. Rep. Rob Andrews and Morristown Mayor Donald Cresitello.
Lautenberg has spent much of the campaign criticizing Andrews' early support for the Iraq war, though Andrews noted that Lautenberg also was an early supporter. Lautenberg and Andrews also clashed over whether Lautenberg, at 84, is too old to serve another term, and whether Andrews, 50, broke protocol by challenging a fellow Democrat.
Lautenberg, of Cliffside Park, was in the Senate from 1983 to 2001, then returned in 2003. Andrews, of Haddon Heights, has been in the House since 1990.
The race has split party leaders, but Lautenberg has the party organization support in Bergen, Essex, Hudson and Middlesex, which account for 41 percent of the state's Democratic voters. Andrews does have some political support in those areas, and hopes to get big support from his South Jersey base.
The winner of that race will face the Republican primary winner - either former U.S. Rep. Dick Zimmer, state Sen. Joseph Pennacchio or former gubernatorial candidate Murray Sabrin - in November.
Each has tried to position himself as a conservative champion of less government spending, with abortion rights being a key difference. Pennacchio and Sabrin oppose abortion; Zimmer supports abortion rights.
Zimmer, 63, has been out of elected politics for a dozen years after losing the 1996 U.S. Senate race and a 2000 House race. He is currently a Washington lawyer and lobbyist.
Pennacchio, 52, has been in the state Legislature since 2001 representing Morris County, the state's second largest Republican county behind Bergen. He is a dentist by trade.
Sabrin is a college economics professor who ran for governor as a Libertarian in 1997 and lost.
Voters will decide contested primaries in seven House districts,
including three where the sitting congressmen are not seeking
re-election:
In Atlantic City, voters will decide a Democratic mayoral candidate among incumbent Mayor Scott Evans, former mayor Lorenzo Langford and former acting mayor Domenic Cappella. The winner will face Republican John McQueen and independents Joseph Polillo and Willie Norwood.