People in Florida began casting their votes for US president on Monday, four years after a debacle in the state held up the 2000 election result.
There were some early glitches with electronic voting
Florida is one of 32 states where voters are allowed to make their choice before election day.
There were some reports of glitches with voting systems, including faulty ballots and a computer crash.
Both John Kerry and George Bush headed to Florida, to campaign in what is again proving to be a key battleground.
Mr Bush won the presidential election after taking Florida by just 537 votes following a controversial count in 2000.
Although the machines that caused confusion last time have been replaced, new electronic voting machines have already had problems.
And both sides have raised the possibility of legal challenges if the outcome is close in Florida or any other battleground.
In Palm Beach County, within an hour of polls opening, a Democratic state legislator claimed to have received an incomplete ballot, saying it was "not a good start".
In Orange County, the touch-screen system crashed.
Elsewhere, queues more than an hour long formed.
Lucien Gennaro, a police aide in Coral Springs, had to leave the queue to get to work, and said: "A lot of people who were waiting just left. I'll try again tomorrow. It was a little frustrating
after what happened in 2000."
Presidential rivals George W Bush and John Kerry have again attacked each other over Iraq and the war on terror, the central theme of the campaign.
Before heading to Boca Raton in Florida, Mr Bush told supporters in New Jersey that Mr Kerry did not understand the threats posed to the US.
He also held a ceremony at the White House to approve $33bn in funding for homeland security.
Correspondents say homeland security continues to be a key concern for voters in this presidential election - the first since the 11 September 2001 attacks - and it is an area where Mr Bush may have an edge.
Mr Bush says he believes he can win normally Democrat New Jersey
He accused Mr Kerry of being stuck in a pre-9/11 mindset.
"Tyrants and terrorists will not give us polite notice before they attack our country," Mr Bush said.
At a rally in Tampa, Mr Kerry switched his focus back to Iraq, from the social security system for senior citizens, which he had accused Mr Bush of planning to privatise.
He referred to a report in the Washington Post that the US commander in Iraq, Lt Gen Ricardo Sanchez, said last winter that his supply situation was so poor that it threatened the troops' ability to fight.
"Despite the president's arrogant boasting that he's done everything right in Iraq and that he's made no mistakes, the truth is beginning to catch up with him," said Mr Kerry.
Various opinion polls show Mr Bush and Mr Kerry at the same level of support nationally.
A Gallup poll for CNN and USA Today suggests Mr Bush is ahead among those who consider themselves likely to vote, but other surveys indicate that Mr Kerry is leading in the vital swing states, according to Reuters news agency.