Tea Party's Rand Paul wins Kentucky Republican primary
Rand Paul: "Tea Party movement is about saving our country from a mountain of debt"
Rand Paul from the conservative Tea Party movement in the US has won the Republican Senate primary in Kentucky.
In Pennsylvania, veteran Senator Arlen Specter fell to Joe Sestak in the Democratic primary.
In both races, endorsements from high profile political figures, including President Barack Obama, failed to sway voters, amid anger at federal politics.
A special election to fill a House seat in Pennsylvania gave the Democrats a boost as they held on to the district.
Analysts are looking at the outcome of Tuesday's ballots as a key indicator of the volatile political mood in America.
In Kentucky, Mr Paul - whose movement is demanding lower taxes and a reduced government - comfortably beat Republican establishment favourite Trey Grayson with some 60% of the vote.
Katie Connolly, BBC Washington reporter
It's tempting to see anti-incumbent sentiment in the defeat of Senator Arlen Specter, but that race says more about the unwillingness of Democrats to embrace the former Republican.
Democrats should worry though, that the vaunted turn-out machine of Democratic Gov Ed Rendell failed to deliver for Mr Specter in Philadelphia. It also casts doubts over the White House's political judgment - they backed Mr Specter from the start.
Anger at Washington is still palpable, as Trey Grayson's loss in Kentucky would suggest.
But in resoundingly rejecting the GOP establishment's preferred candidate and embracing ultra-conservative Tea Party-supported Rand Paul, Kentucky Republicans may have given Democrats a shot at taking the seat in November.
There's one real bright spot for Democrats.
Their victory in the election to replace the late Democratic House Representative John Murtha proved that in races without an incumbent, a well-oiled campaign machine - including a high-profile visit from Bill Clinton - can overcome their downward trend in national polls.
Mr Grayson had the backing of Mitch McConnell, the Republicans' leader in the Senate, as well as local Republican leaders.
"[Voters] don't want the same old, same old politicians and I think they think the system is broken and needs new blood," Mr Paul said of his win.
Sarah Palin, the former vice-presidential candidate who was backing Mr Paul, told the Associated Press that his victory was a "wake-up call for the country".
Mr Paul and Mr Grayson were vying for the Republican nomination for a Senate seat vacated by retiring Senator Jim Bunning.
There was a similar upset in the Democratic primary in Pennsylvania. Mr Specter, a Republican senator since 1980 who switched parties last year, was beaten by Representative Joe Sestak.
"This is what democracy looks like," Mr Sestak said after his victory. "A win for the people over the establishment, over the status quo, even over Washington DC."
In the Arkansas Senate primary, incumbent Blanche Lincoln did not get enough votes to avoid a run-off on 8 June against Lieutenant Governor Bill Halter.
Ms Lincoln's support for the economic bailout and healthcare reform angered Arkansas conservatives, while liberals criticised her for not supporting energy legislation designed to curb greenhouse gas emissions.
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