Two veterans of Minnesota politics, back in the spotlight after big wins in the primary election, are bringing different approaches to the task of unseating congressional incumbents in November.

Democrat Rick Nolan and Republican Allen Quist won congressional primaries Tuesday night after decades out of public office. Nolan, who served in Congress from 1975 to 1981, will challenge first-term GOP Rep. Chip Cravaack in northeastern Minnesota’s 8th District. Quist, a well-known conservative activist who served in the state House from 1983 to 1989, will take on Democratic Rep. Tim Walz in southern Minnesota’s 1st District.

Nolan, 68, said he would run on ending tax cuts for the wealthy and investing more in schools, roads and other priorities. Quist, 67, drew a line against tax increases and said balancing the federal budget would be his campaign’s chief message.

Both will face incumbents likely to raise more money. Asked if he was the underdog, Quist said: “It’ll be billed that way. But we don’t see it that way.” He pointed out that Walz got 49 percent of the vote in a three-way race in 2010, and that this year’s contest would be a two-way matchup.

The 1st District, with many rural areas but also cities including Rochester, Mankato and Winona, has long been a political swing area. But Walz, first elected in 2006, has built a formidable base of support.

Walz’s campaign released a statement congratulating Quist and saying Walz has “stood up for middle class families, veterans, students and seniors.”

In the 8th, Democrats see a chance to win back a seat they didn’t think they would lose two years ago, when Cravaack upset longtime Rep. Jim Oberstar in what the party sees as its turf.

“It’s very difficult to defeat an incumbent member of Congress under any circumstances,” Nolan said. “I don’t think I go in as the favorite, but it’s definitely winnable for a Democrat.”

Cravaack also congratulated Nolan on his win, and said he’d campaign to cut spending, reduce government regulations and bring jobs to the district.

In the primary, Quist beat state Sen. Mike Parry with 54 percent to Parry’s 46 percent. Nolan beat two Democrats, winning 38 percent of the vote to 32 percent for former state senator Tarryl Clark and 29 percent for Jeff Anderson, a former Duluth city councilman.

After serving in the state House in the 1980s, Quist lost the 1994 Republican primary for governor to incumbent Arne Carlson despite winning the party endorsement that year. The Parry campaign trotted out some of his past controversial statements, including a 1994 interview where he said men had a “genetic predisposition” to lead households.

But Parry’s run was rocky, too. The week before the election, he was sharply criticized after accusing Gov. Mark Dayton, a Democrat, of popping pills in a meeting.

Nolan, who had the Democratic endorsement in the race and support from Gov. Mark Dayton and other party luminaries, nevertheless had to battle perceptions that he wasn’t much different from Oberstar. The two were both first elected in 1974, leading state GOP Chairman Pat Shortridge to ridicule the two as “Watergate babies.”

Clark enjoyed a large fundraising advantage over Nolan, including the most support from outside groups. But she carried the burden of having moved into the district after losing in 2010 to U.S. Rep. Michele Bachmann in a central Minnesota district, and her opponents tagged her as an outsider.

In other primary action, Sen. Amy Klobuchar and Kurt Bills breezed to easy primary victories in the U.S. Senate race, setting up a general election contest between the Democratic incumbent and a Republican challenger new to statewide politics.

Klobuchar had only token opposition. Bills, a first-term state representative and high school teacher who carried the GOP’s endorsement, rolled past two rivals. Stephen Williams, of the Independence Party, will make it a three-way race in November.

In other House races, Reps. Bachmann, Erik Paulsen, John Kline, Keith Ellison and Betty McCollum easily staved off primary challengers. In McCollum’s St. Thomas-area district, businessman Tony Hernandez won the GOP primary to take her on.

The House and Senate races weren’t alone on the ballot. Forty-four legislative primary races were under way, including three western suburban Twin Cities districts where Republican incumbents faced conservative challengers as they sought to move up or defend their seats. One of those, state Rep. Steve Smith, was a casualty, falling to tea party challenger Cindy Pugh.

It’s only the second time Minnesota has held its primary election in August since moving it up from September to give military and overseas voters more time to vote in the general election. But it’s the first since the state redrew its congressional and legislative district boundaries to reflect population shifts.

Also up were two Minnesota Supreme Court races, where the top two vote-getters will advance to the November election. Two incumbents, Chief Justice Lorie Skjerven Gildea and Justice David Stras, both advanced in their races. Gildea will face International Falls attorney Dan Griffith, while Stras will face Bemidji magistrate Tim Tingelstad.