Arizona Sen. John McCain and former Massachusetts Gov. Mitt Romney, who have been leading in polls, traded final barbs as voting began. They have been locked in a seesawing battle to be the party's candidate for the November presidential election.
Giuliani has staked his campaign on a strong showing in Florida after largely ignoring other states that held nominating contests earlier this month.
But polls have shown him trailing both nationally and in this state with a large population of retired New Yorkers as McCain and Romney picked up momentum from earlier wins.
Voting is scheduled to wrap up at 7 p.m. EST (2400 GMT) in most of Florida and an hour later in the northwestern part of the state. Results usually emerge soon after.
A Reuters/C-SPAN/Zogby poll released early on Tuesday showed McCain with a slim 35 percent to 31 percent lead over Romney. Giuliani and former Arkansas Gov. Mike Huckabee were tied for third place with 13 percent each in the poll, which had a margin of error of 3.3 percentage points.
About one million absentee and early-voting ballots have already been cast, a factor that could help Giuliani given his intense campaigning in the state while rivals were elsewhere.
The winner in Florida will gain valuable momentum heading into the Feb. 5 "Super Tuesday" voting, when 21 states will have Republican nominating contests in a coast-to-coast battle.
. At a delicatessen in a Miami suburb on Tuesday morning, Giuliani talked optimistically about moving on to other states after the Florida contest.
"We are going to win today," he said flatly. "Polls and predictions have been wrong." McCain and Romney have dominated the headlines in Florida with a heated battle over who is best prepared to rescue a struggling economy and lead a country that is at war in Iraq and Afghanistan. McCain has made gains since his endorsement on Saturday by Florida Gov. Charlie Crist.
McCain questioned Romney's economic record in Massachusetts and lack of foreign policy experience at a polling station in St. Petersburg.
"Who it is that has got the background and knowledge to take on radical Islamic extremism?" McCain said. "I think that's where the people of Florida will make the judgment on my behalf."
Romney, a former venture capitalist, touted his business acumen and painted McCain, who has been in the Senate for more than two decades, as an out-of-touch career politician.
"To fix Washington you can't just send back Washington politicians who have spent their whole career there and just move them into different chairs," he told a rally in Tampa.
McCain and Romney have split the last four nominating contests. McCain has won in South Carolina and New Hampshire and Romney has carried Michigan and Nevada. Huckabee won the kick-off contest in Iowa.
Florida's Democratic contest has been discounted by the national party because the state scheduled it earlier than party rules allow, and Democratic candidates have avoided campaigning here.
Still, Democrat Hillary Clinton plans to visit the state after polls close in a bid to claim at least a symbolic victory in a state where the New York senator and former first lady is expected to beat leading rival Barack Obama.
Obama, an Illinois senator, is coming off a commanding victory in South Carolina on Saturday and an endorsement on Monday by Massachusetts Sen. Edward Kennedy, scion of the country's best-known Democratic political dynasty.
Obama was to visit his maternal grandfather's hometown in the largely rural state of Kansas in a bid to reach out to voters in Republican-leaning states. Obama, who would be the first black president, is the son of a Kenyan father and a white American mother.