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After an exhausting, wild, bitter, and sometimes sordid campaign, Americans finally began voting Tuesday for a new president: either the billionaire populist Donald Trump or Hillary Clinton, seeking to become the first woman to win the White House.

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Early-rising voters in nine states mainly along the East Coast got first crack at a pivotal election that has a nervous world watching closely after a campaign like no other.

The name of the winner was not expected to be known before 0300 GMT. Clinton has a slim lead in the polls but no one was ruling out a Trump victory.

Democratic frontrunner Clinton and Republican maverick Trump campaigned into the early hours of election day, presenting radically different visions of the future of the world's biggest power as they capped a grueling final day of wooing voters.

The 69-year-old former first lady, senator and secretary of state -- backed by A-list musical stars and incumbent President Barack Obama -- urged the country to unite and vote for "a hopeful, inclusive, big-hearted America."

Trump meanwhile pressed his message with voters who feel left behind by globalization and social change, wrapping up with a flourish on his protectionist slogan of "America first."

"Just imagine what our country could accomplish if we started working together as one people, under one God, saluting one American flag," the 70-year-old former reality television star told cheering supporters.

Some 40 million Americans have already cast ballots in states that allow early voting, and opinion polls suggest Clinton has a slight edge.

In a kick-off midnight vote, the residents of tiny Dixville Notch in New Hampshire cast their traditional first-in-nation ballots with a total of eight votes -- Clinton getting four and Trump, two.

The others went to a fringe candidate and Mitt Romney, the failed Republican hopeful in 2012.

A polling average by tracker site RealClearPolitics gave Clinton a 3.3-percentage point national lead, but Trump is closer or even has the advantage in several of the swing states that he must conquer to pull off an upset.

- 'Corrupt elite' -

No results or exit polls will be available before polling stations begin to close on the US East Coast from 7:00 pm (0000 GMT Wednesday), and it may be three or more hours after that before the direction of the race becomes clear.

And even then, questions remain. Trump has repeatedly warned that a "corrupt Washington and media elite" is seeking to rig the race and he said last month that he may not concede defeat if he thinks voting is unfair.

He has also threatened to lodge lawsuits against up to a dozen women who have come forward during the race to accuse him of sexual assault or inappropriate behavior.

Clinton has pushed a more optimistic vision, despite a wobble in the final weeks of her campaign when the FBI reopened an investigation into whether she had put US secrets at risk by using a private email server -- only to close the probe again on Sunday.

In a radio interview on the last night of the campaign, she said the matter was behind her, and she courted voters at her final rallies in Philadelphia with Obama and rocker Bruce Springsteen, and in North Carolina with pop diva Lady Gaga.

"Tomorrow, we face the test of our time," she declared in front of 40,000 people in Philadelphia, a record for her in a campaign where despite her opinion poll lead she has struggled to match her Republican opponent's passionate and raucous crowds.

- 'I will fight for you' -

"There is a clear choice in this election. A choice between division or unity, an economy that works for everyone, or only for those at the top; between strong, steady leadership, or a loose cannon who could put everything at risk."

At the same time, Trump, who hijacked his conservative party and turned it into a vehicle for populist bombast, concluded a last-gasp tour of swing states by painting his rival as doomed to defeat and the corrupt creature of a discredited elite.

"Do you want America to be ruled by the corrupt political class, or do you want America to be ruled, again, by the people?" he demanded at a rally in New Hampshire, a state Obama won in 2012 that Trump hopes to flip into his column.

Promising to end "years of betrayal," tear up free trade deals, seal the border, halt the drug trade and subject Syrian refugees to "extreme vetting", Trump told his supporters: "I am with you and I will fight for you and we will win."

Voters on Tuesday are also electing candidates for 34 seats in the 100-member Senate and the entire 435-member House of Representatives, as well as deciding on state ballot initiatives around the country.

Trump's campaign spooked world markets seeking stability after the recent global slowdown.

Last week, US stocks as measured by the S&P 500 index fell for nine straight days for the first time since 1980, only to recover a little when the FBI confirmed Clinton would not face prosecution over her emails.

Asian markets were up slightly on Tuesday as the world remained on tenterhooks for the result.