After the longest, most expensive election campaign in US history, voters are about to elect the 44th president.
Republican John McCain and Democrat Barack Obama have returned to their home states of Arizona and Illinois to vote and hold final rallies.
Mr Obama is holding a steady lead in final opinion polls and record numbers of voters are expected to turn out.
In the first voting of the day, Mr Obama defeated his rival by 15 votes to six in Dixville Notch, New Hampshire.
The town, which has a 60-year tradition of being first in the nation to vote, opened its polls at midnight, with turnout of 100%.
George W Bush won there in 2004 on his way to re-election. Tuesday’s vote was the first time the town had gone Democrat since 1968.
Another small New Hampshire town, Hart’s Location, with a tradition of polls opening at midnight, has also gone for Mr Obama by 17 votes to 10.
Most other polls on the east coast will open at 0600 EST (1100 GMT).
Tributes to grandmother
After he spent Monday criss-crossing the country visiting seven crucial states, Mr McCain continued his campaigning into election day with an early morning stump speech in Prescott, Arizona.
He promised supporters that he and his running-mate Sarah Palin would “change things in Washington”.
On the eve of the ballot, the Alaska governor was cleared by a state inquiry of violating ethics law.
At his final rally in the suburbs of Washington, DC, Mr Obama appeared before a crowd of 100,000 people.
The man running to be the first African-American president of the US spoke of national unity just a few miles from the scene of the opening battle of the American Civil War.
Earlier in the day, Mr Obama said his grandmother, Madelyn Dunham – who largely raised him as a child – had died aged 86 in Hawaii after losing her battle with cancer.
In a joint statement with his half-sister, he described her as “the cornerstone of our family, and a woman of extraordinary accomplishment, strength, and humility,” adding that their debt to her was “beyond measure”.
Senator McCain and his wife Cindy issued a statement offering their deepest condolences to Mr Obama and his family.
At an event in North Carolina, Mr Obama appeared emotional as he spoke of his grandmother, saying she had died peacefully in her sleep with his sister by her side.
At his speech in the Washington suburb of Manassas, Virginia, he told supporters that he had found the long journey to election day both humbling and enriching.
“You’ve filled me with new hope for our future and you’ve reminded me about what makes America so special.”
A USA Today/Gallup poll published on Monday found likely voters favour Mr Obama by 11 points over Mr McCain, 53-42%.
Other national polls indicate Mr Obama’s lead over his rival is holding steady at between five to 11 percentage points.
But the BBC’s James Coomarasamy, in Washington, says that while Mr Obama has held a consistent lead for several weeks, a number of factors could undermine the pollsters’ predictions.
Among them, he says, are the role the Illinois senator’s skin colour may play in voters’ intentions; whether newly-registered voters will actually vote; and the Palin effect – whether Mr McCain’s running mate has energised or alienated Republicans.
On Monday, an investigator for the Alaska Personnel Board cleared her of violating state ethics laws as governor of Alaska.
A separate report released last month found that she did abuse her office by allowing her husband and staff to pressure Alaska’s top law enforcement official to fire her former brother-in-law.
Mrs Palin sacked Walt Monegan, the state public safety commissioner, but denied it was because of his refusal to dismiss her sister’s ex-husband, a state trooper.
Both camps were keenly aware of the need to get voters out in the states that polls suggest remain in the balance.
Mr McCain dashed through half a dozen states on the marathon campaign’s final day – including Florida, Tennessee, Pennsylvania, Indiana, New Mexico and Nevada – before heading home to Arizona.
Various polls suggest Mr Obama has a two- to four-point lead over him in electoral vote-rich Florida.
On Monday morning, the 72-year-old told a crowd of about 1,100 supporters in Tampa, Florida: “Senator Obama is running to spread the wealth, I’m running to create more wealth.”
Mr Obama, 47, spent Monday targeting states that four years ago voted Republican but where he now has a chance of winning, including Virginia and North Carolina, which have not backed a Democratic hopeful in decades.
Both campaigns have thousands of volunteers working flat-out manning phone banks, handing out brochures and knocking on doors ahead of Tuesday’s election.
Some 130 million Americans are expected to vote, in a higher turnout than in any election since 1960, the BBC’s North America editor Justin Webb says.
A record 27 million people had already cast absentee or early ballots as of Saturday night.
Under America’s Electoral College system, states are apportioned votes based on their population, the biggest being California with 55 votes.
A candidate needs to gain 270 out of the 538 Electoral College votes to win the presidency.
Polls suggest the six closest state races on election day will be in Florida, Indiana, Missouri, North Carolina, Nevada and Ohio.
Mr McCain holds the lead in Indiana and North Carolina, but Mr Obama is ahead in the others, the latest polls from Reuters/C-SPAN/Zogby suggest.
When Americans go to the polls, as well as choosing a new president and members of Congress, they will be casting votes on a wide range of ballot initiatives such as same-sex marriage, abortion and animal rights.
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