By ABBY GOODNOUGH
 
IAMI, Oct. 16 - Defining the Hispanic vote in Florida used to be easy: Cuban immigrants, Republican to the last. But just try boiling it down this election season.

A huge influx of Puerto Ricans, Mexicans and people from Central and South America has diluted the political clout of Cubans, loosening the Republican lock on the Hispanic vote. The state has an estimated 650,000 Puerto Ricans, for example, a group that usually leans Democratic, up from 481,000 in 2000.

Colombians, Puerto Ricans and Dominicans are leaning toward Senator John Kerry, polls suggest, though many have registered as independents and the Democrats do not consider their vote a sure thing. Nicaraguans embrace President Bush, and Cubans, while still overwhelmingly Republican, may throw some support to the Democrats for a change.

Little wonder, then, that Florida's 3.2 million Hispanic residents - the state's largest minority group, tens of thousands of whom will be first-time voters next month - are among the most coveted voters in the nation this year.

"The message for both parties is, these people can go either way and you've got to work it," said Jorge Mursuli, national director of Mi Familia Vota, a voter registration group that signed up 73,000 Hispanic voters here this year, 40 percent as independents.

Both presidential candidates are feverishly courting the Florida vote as the campaign comes down to the wire - Mr. Bush held three rallies here Saturday and will return Monday and Tuesday, while Mr. Kerry is to campaign in Florida on Sunday and Monday.

Republicans and Democrats have scoured the state to find new citizens, focusing on South Florida, where Central and South Americans have joined the large Cuban contingent, and Central Florida, home to a fast-growing Puerto Rican population. Even finding these potential voters is a challenge, strategists say, because many now scatter through suburbs instead of clustering in urban neighborhoods like Little Havana in Miami.

And unlike blacks, who vote more often as a bloc, Hispanics bring a patchwork of priorities to the electoral table. Cubans care deeply about how Washington deals with Fidel Castro - though even they cannot be defined singularly this year, as many newer arrivals are angry about Mr. Bush's Cuba policy. Puerto Ricans want to know a candidate's stance on whether their homeland should become a state. Racial discrimination is a big issue for Hispanics in Central Florida, Mr. Mursuli said, while those in South Florida, whose Latino community is larger and more established, do not experience it as much.

Both parties believe Mr. Bush will win the majority of Hispanic votes in Florida, if only because the Cuban population remains so large - about 450,000 registered voters, compared with about 200,000 for the second-biggest group, Puerto Ricans. But Democratic strategists say their party is pushing for Mr. Kerry to win perhaps 40 percent of the Hispanic vote, potentially a big enough increase over the roughly 34 percent that Al Gore claimed in 2000 to assure a Democratic victory here.

Both campaigns consider Puerto Ricans particularly up for grabs because so many are newly registered and have not formed party loyalties. They supported Mr. Gore in the 2000 presidential election, but went for Gov. Jeb Bush, a Republican, in his 2002 re-election bid. The conventional wisdom is that the governor appealed to Hispanics more than Bill McBride, his little-known Democratic opponent, because he constantly visited their neighborhoods, speaking fluent Spanish and presenting himself as their friend.

Though Jeb Bush has not done much stumping for his brother, the president, in Hispanic communities - or anywhere, for that matter, because the four hurricanes that devastated large swaths of the state have preoccupied him this campaign season - he made several visits to Puerto Rican communities that were hard hit by the storms, promising financial and emotional support.

And this year, President Bush has another Spanish-speaking surrogate courting Florida Hispanics: Mel Martinez, a Cuban-American who is Mr. Bush's former housing secretary and the Republican candidate in the race for the seat of Senator Bob Graham, a Democrat who is retiring.

On Friday, the Bush-Cheney campaign said that Al Cardenas, a Cuban-American and former Florida Republican Party chairman, would join Jeb Bush as a co-chairman of the president's campaign here.

"He wanted to come in and help close the deal, especially as it relates to Hispanics," said Alberto Martinez, a spokesman for the Bush campaign here.

"The presence of Jeb Bush and Martinez will make the president a very tough competitor when it comes to fighting for that Central Florida vote," said Sergio Bendixen, a Democratic pollster in Miami. "The Democrats are fighting there with issues, without any personalities. The Republicans are fighting with personalities, with very few issues."

The Bush campaign has run 10 television advertisements in Spanish, some touching on issues like health care and education but others simply painting Mr. Bush as a kindred spirit to Latinos. One plays a song describing him as "someone who knows my problems, my culture," adding, "I'm with Bush because he knows my family."

Mr. Kerry has run fewer advertisements in Spanish, but the New Democratic Network, a Democratic advocacy group, has filled in the gap. Among its anti-Republican advertisements are two aimed at Cuban voters, many of whom have condemned a new policy limiting them to one trip home every three years and restricting cash transfers and gift packages to Cuba.

In one New Democratic Network ad, a Cuban-American woman asks: "How long will they keep brainwashing us? Cuba's problem is something that we, the Cubans, need to resolve. And in the meantime, what are the Republicans doing to solve the problems we have here?"

Still, even the most optimistic Democrats predict that only a small fraction of Cuban voters will switch allegiances in November, especially because Mr. Martinez is on the Republican ballot. In a poll last month for the New Democratic Network, Mr. Bendixen found that 72 percent of Cuban voters supported Bush, compared with 19 percent for Mr. Kerry and 9 percent either undecided or for Ralph Nader.

The same poll, of 800 Hispanic voters in Florida, had 35 percent of non-Cuban Hispanics supporting Mr. Bush, 59 percent Mr. Kerry and 6 percent undecided or supporting Mr. Nader.

A new poll of 800 Florida Hispanics by The Washington Post, Univision and the Tomas Rivera Policy Institute found Mr. Bush leading Mr. Kerry by 61 percent to 32 percent. Mr. Bush drew 81 percent of the Cuban vote, while Mr. Kerry won 42 percent of the Puerto Rican vote and 48 percent of Hispanics who were not Cuban or Puerto Rican.

Random interviews in Miami on Friday demonstrated just how disparate the Hispanic electorate can be. Belkys Gomez, a Cuban-American who works in billing at the University of Miami, said she was still undecided but would probably vote for Mr. Bush.

"The only thing that throws me towards Bush is that I know him," Ms. Gomez, 40, said. "We have a saying in Spanish that says something like 'A bad well known is better than a bad to be known.' No one really knows who Kerry is."

Jose Lugo, a funeral director who is Puerto Rican, said he strongly preferred Mr. Kerry. Of Mr. Bush, he said: "I don't like the way he is conducting the war. I was in the Army for seven years and I don't think he should have rushed into war."

Jeanine Escobar, a restaurant owner from Nicaragua, said she was absolutely for Mr. Bush. "He is against communism and I come from a country that knows communism," she said. "It's not that I dislike Kerry, but he doesn't have our same ideology."