US election: Results declared from some states
President Barack Obama and challenger Mitt Romney remain locked in a tight race as US election results stream in.
Mr Obama has won swing states Michigan and Pennsylvania, as well as many others he won in 2008.
Mr Romney, a Republican, took North Carolina and Indiana from Mr Obama, as well as other solid Republican states.
Tens of millions of voters cast ballots on Tuesday. The winner could be declared shortly as more swing states begin reporting results.
Pre-election polling suggested a neck-and-neck race but gave the president a slender lead in some swing states.
Polling stations began closing in eastern states at 18:00 EST (23:00 GMT), with the crucial states of Virginia and Ohio closing at 19:00 EST and 19:30 EST respectively.
The race in Florida, which is considered critical especially to Mr Romney, remains too close to call with more than 90% of precincts reported.
In those states and elsewhere, election workers at polling stations with long queues allowed voting to continue past the official closing.
In one of the first swing states to fall, Mr Obama won Michigan, repeating his 2008 victory there.
Mr Romney's father George was governor of Michigan in the 1960s and Mitt Romney was born and raised there.
But the president's 2009 rescue of the car industry helped seal the deal with the state's voters, analysts say.
Mr Obama also took Pennsylvania, continuing a Democratic streak dating back to 1992. He also held New Hampshire and Minnesota, states he won in 2008 but which the Republicans hoped to take from him.
The president also won in Wisconsin, the home state of Republican vice-presidential candidate Paul Ryan, a congressman.
The Republican party last won the state in 1984 with Ronald Reagan, but hoped this year that Mr Ryan would make it competitive.
Mr Romney won Indiana and North Carolina, the only two states so far that have switched hands from 2008, when Mr Obama narrowly won them.
Elsewhere, Mr Romney won Alabama, Arizona, Arkansas, Georgia, Idaho, Kansas, Kentucky, Louisiana, Missouri, Mississippi, Montana, Nebraska, North Dakota, Oklahoma, South Carolina, South Dakota, Tennessee, Texas, Utah, West Virginia and Wyoming.
Mr Obama has taken California, Connecticut, Hawaii, Illinois, Maine, Maryland, Massachusetts, New Jersey, New Mexico, New York, Oregon, Pennsylvania, Rhode Island, Vermont, Washington state and Washington DC.
After a hard-fought race that began nearly two years ago and cost more than $2bn (£1.3bn), national polls by Washington Post/ABC News and the Pew Research Center both give Mr Obama a three-point edge over his rival.
In areas of New Jersey and New York that were damaged by storm Sandy a week ago, turnout was described as heavy. One high school being used as a shelter for displaced families doubled up as a voting centre.
Across the US, voting took place against a variety of backdrops - from a launderette and an internet cafe in Chicago to a lifeguard station in Los Angeles and car dealership in Columbus, Ohio.
Obama 'very good'
Mr Obama was the first of the two rivals to cast their ballot by voting last month in his adopted home city of Chicago, and becoming the first sitting president to vote before election day.
Mr Romney and his wife Ann voted in the Boston suburb of Belmont, Massachusetts, shortly before 09:00 local time on Tuesday. He told reporters he felt "very good".
The election is decided by the electoral college.
Each state is given a number of electoral votes in rough proportion to its population. The candidate who wins 270 electoral votes - by prevailing in the mostly winner-take-all state contests - becomes president.
Also on Tuesday's ballot are 11 state governorships, a third of the seats in the 100-member US Senate and all 435 seats in the House of Representatives.
Republicans are expected to keep control of the House, while Democrats are tipped to do the same in the Senate.
Legal battles feared
With voter turnout seen as vital for both candidates, campaigning continued on Tuesday, but at a slower pace.
Both men gave radio interviews, and Mr Romney hit the campaign trail again, with visits to Ohio and then Pittsburgh, Pennsylvania.
Analysts tried to determine whether Mr Romney's last-minute campaigning showed strength or desperation, while the candidate reportedly told aides he wanted to be active on election day instead of just sitting around waiting for results.
The Republican was due to return to Boston later for an election night rally.
Mr Obama, who will hold an election night rally at a convention centre in Chicago, visited a campaign office in the city to talk to volunteers. He praised his Republican rival's "spirited campaign".
With observers anticipating a close race, both sides have readied teams of lawyers for possible legal fights, especially in the critical battleground state of Ohio.
Some analysts fear the election will not be decided on Tuesday night if the state's vote becomes mired in legal battles.
The BBC is providing full online live results of the US presidential election. More details here .
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