Voters have been streaming into polling stations in the key New Hampshire presidential primary, fuelling expectations of a record turnout.
New Hampshire hamlet Dixville Notch has already voted
The state secretary, Bill Gardner, has predicted that at least half a million people will cast their ballots.
The first votes counted, and opinion polls, put Barack Obama and John McCain ahead in their respective races.
Candidates are aiming to build momentum before more than 20 states hold polls on 5 February, known as Super Tuesday.
Analysts say New Hampshire's large bloc of independents - about 45% of registered voters - could be key to swinging the primary, the second in a series of state-level votes and caucuses through which the parties choose their candidates for the US presidency.
Mr Obama, in particular, showed strong appeal at last week's Iowa caucuses among such voters, who are registered as neither Republican nor Democratic.
The BBC's Justin Webb in New Hampshire says Mr Obama's team are now expecting a "crushing victory" in the state.
While Iowa and New Hampshire - two of the earliest contests - do not necessarily produce a winner, they can boost contenders' chances of winning ahead of primaries in larger states.
Two tiny hamlets, Dixville Notch and Hart's Location, traditionally the first to vote in New Hampshire, opened their polling stations at midnight giving small, early victories to Mr Obama and Mr McCain.
Most of the rest of the state began voting at 0600 local time (1100 GMT). Polls close at 2000 (0100GMT Wednesday) and first results are expected shortly afterwards.
Turnout has been exceeding expectations, helped by unusually mild weather for this time of year in New Hampshire.
New Hampshire Deputy Secretary of State Dave Scanlan told ABC News that turnout is "absolutely huge, and towns are starting to get concerned that they don't have enough ballots".
Candidates from both parties have been speaking at a number of campaign events throughout the state.
At a rally at Dartmouth College, Mr Obama told cheering supporters: "Today you can make your voice heard - you can insist that change will come.
"The American people have decided for the first time in a very long time to cast aside cynicism, to cast aside fear, to cast aside doubts."
Democrat Senator Hillary Clinton and the Republicans Rudy Giuliani and Mike Huckabee were among the candidates who turned up at polling stations throughout the day in last-minute bids for votes.
CURRENT KEY DATES
8 Jan: New Hampshire primary
15 Jan: Michigan primary
19 Jan: Nevada caucuses; South Carolina primary (Rep)
26 Jan: South Carolina primary (Dem)
29 Jan: Florida primary
5 Feb: some 20 states including California, New York, New Jersey
After finishing third in Iowa, the former first lady Mrs Clinton is trailing Mr Obama by as many as 13 points in one state-wide opinion poll.
Joined by her daughter, Chelsea, and husband, former President Bill Clinton, Mrs Clinton said she was feeling "really good" and was "going to work all day to get the vote out".
Excited crowds waited to greet her at a polling station at a school in Concord. Among them were dozens of children, with whom she posed for pictures, as well as local voters.
Mrs Clinton has seen her lead in the polls eclipsed by Mr Obama but has vowed to "go on".
'Starting below the bottom'
Mr Huckabee, who is currently polling third in the Republican contest, was in a jocular mood, even asking Rudy Giuliani for his vote.
"We started below the bottom. For us to come in the top four would be a win for us," said the former Arkansas governor and Baptist minister, who was a virtual unknown until recently.
Arriving at the site moments later, Republican contender Mitt Romney said: "The Republicans will vote for me. The independents will get behind me."
John McCain has resumed his lead in the polls
After a disappointing second-place showing behind Mr Huckabee in Iowa, Mr Romney needs a strong showing in New Hampshire to keep his campaign alive.
Both are threatened by a resurgent Mr McCain who, after seeing his campaign nearly derail last summer, has concentrated much of his time and money on New Hampshire.
Other Republican candidates have been looking beyond the New Hampshire primary to focus on states that go to the polls later.
Former New York mayor Mr Giuliani has been focusing on Florida's 29 January contest, hoping to gain momentum going into Super Tuesday.
Actor and former Senator Fred Thompson has been campaigning in South Carolina, where Republicans vote on 19 January.
You can watch live coverage of the results in the New Hampshire primary on the BBC News website from 2000 (0100 GMT)