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Republicans had to deal with retirements only in Arizona, Texas and Maine. But the GOP’s plans suffered huge setbacks when its candidates in Missouri, Rep. W. Todd Akin, and in Indiana, state Treasurer Richard Mourdock, made controversial remarks about rape and abortion.

Mr. Akin, seeking to oust Democratic incumbent Claire McCaskill, told an interviewer in August that women’s bodies have a way of rejecting pregnancy in cases of “legitimate rape.” Mrs. McCaskill retained her seat.

Mr. Mourdock, who defeated six-term Sen. Richard G. Lugar in the GOP primary, said during a televised debate last month that a pregnancy resulting from rape was something “God intended.” He lost to Democratic Rep. Joe Donnelly.

Other Senate races included the contest in Nebraska to replace retiring Democrat Ben Nelson, who opted not to run after casting the deciding vote for President Obama’s health-care bill in 2010. Republican state Sen. Deb Fischer defeated Democrat Bob Kerrey, a former senator and governor. For much of the campaign, the Republican had led in the polls.

In North Dakota, Democrats nominated former state attorney general Heidi Heitkamp to replace retiring Sen. Kent Conrad, a Democrat first elected in 1986. Republicans nominated Rep. Rick Berg, who had led in most polls.

In Wisconsin, Democratic Rep. Tammy Baldwin, an openly gay member of Congress, won the race to replace retiring Democrat Herb Kohl, defeating former Republican Gov. Tommy G. Thompson, who acknowledged not having much energy for a vigorous campaign.

In Montana, Democratic Sen. Jon Tester appeared headed to victory over Republican Rep. Denny Rehberg, the state’s lone congressman. Mr. Rehberg, a former lieutenant governor, lost a bid for the Senate in 1996 to incumbent Democrat Max Baucus.

Republicans were fighting to hold onto the Senate seat in Nevada, where incumbent Sen. Dean Heller was running against Democratic Rep. Shelley Berkley.

In Pennsylvania, a late charge by Republican nominee Tom Smith, who made a personal fortune in the coal industry, fizzled against Democratic Sen. Bob Casey, son of the late governor.