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“We congratulate Christine ODonnell for her nomination this evening after a hard-fought primary campaign in Delaware,” said NRSC Executive Director Rob Jesmer.

In an unusually rough GOP primary, O'Donnell supporters have suggested the moderate Mr. Castle, 71, is so frail that he might die before finishing his Senate term, that he might switch parties and even floated rumors about his sexual orientation.

Mr. Castle and the state GOP responded with ads criticizing Ms. O’Donnell, 41, for lying about her education and record, leaving a trail of unpaid bills that included unsettled campaign debts, tax liens and a default on her mortgage, and using campaign finances for personal expenses.

“I am very proud of the integrity and the honesty of everyone who has been involved in my campaign,” a subdued Mr. Castle said. “The last several weeks have been spirited, shall we say.”

Ms. O'Donnell, during her victory speech, pleaded for the support of Castle voters.

“If those same people who fought against me work just as hard for me, we will win,” she said.

Ms. O'Donnell will face Democratic New Castle County Executive Chris Coons, 47, in November. Polls show the Democrat holds a comfortable lead over Ms. O'Donnell, but suggested he would have lost to Mr. Castle by double digits.

The Republican cross-currents in the New Hampshire race were not as clear, as Mrs. Ayotte enjoyed backing from Mrs. Palin, while other leading conservatives went with Mr. Lamontagne. But the former state attorney general was widely seen as the stronger candidate to hold the seat being vacated by GOP Sen. Judd Gregg.

Mr. Lamontagne, who also benefited from tea party support, held an early lead with 44 percent of the vote with about 20 percent of the precincts counted, while Mrs. Ayotte was second with 36 percent.

The winner will face Democratic Rep. Paul W. Hodes, who is giving up his seat in the House to run for the Senate.

In New York, Mr. Rangel hoped voters would reserve judgment on an ethics investigation and put him on track for a 21st term.

Mr. Rangel held an early lead late Tuesday over his principal primary challenger, Adam Clayton Powell IV, a state assemblyman whose father the incumbent beat 40 years ago. In the decades since, Mr. Rangel rose to become chairman of the powerful House Ways and Means Committee, a post he was forced to give up in the face of the ethics probe.

In Wisconsin’s Republican gubernatorial primary, Milwaukee County Executive Scott Walker held a 3 percentage-point lead over former Rep. Mark Neumann with 22 percent of the precincts counted.

In Rhode Island, Providence Mayor David N. Cicilline was declared the winner against three other Democratic primary candidates for the open House seat held by retiring Democratic Rep. Patrick J. Kennedy. Mr. Cicilline will face Republican state Rep. John Loughlin II.

Staff reporter Joseph Weber and the Associated Press contributed to this report.