On the eve of the U.S. presidential election, public-opinion polls indicate a very close race between the Republican incumbent, President George Bush, and his Democratic challenger, Massachusetts Senator John Kerry. 

The latest Gallup poll has President Bush and Senator Kerry tied at 49 percent each.  In the final hours, the candidates appealed to both core supporters and a dwindling pool of undecided voters.

President Bush is counting on a strong turnout from those who support his handling of the war on terrorism.

"Even when you might not agree with me, you know what I believe, where I stand and what I intend to do," Mr. Bush says.

Senator Kerry made his own furious last-minute push for votes in several key swing states, trying to assure voters that he too would be a strong leader in the war on terrorism.

"We need a president who can defend America, yes, but who can also stand up and do what is right and fight for the middle class and people trying to get into it," Mr. Kerry says.

As voters head to the polls, they have much to consider about the strengths and weaknesses of both candidates.

Polls suggest that voters have more confidence in President Bush than Senator Kerry on the issue of terrorism.  But they are split on the president's handling of Iraq and seem to give the edge to Senator Kerry on domestic issues like jobs and health care.

Karlyn Bowman, who monitors national and state polls at the American Enterprise Institute in Washington, says: "Bush maintains a strong lead in nearly every poll on dealing with terrorism.  John Kerry has regained the lead as the candidate who can better handle the economy, something he had to do to be competitive in this race."

In the final weeks of the race, both candidates spent most of their time campaigning in a small group of so-called battleground states where the election appears to be very close.

These key states include Pennsylvania, Florida, Ohio, Iowa, Wisconsin, New Hampshire, and New Mexico.

Polls suggest most of the other states are leaning toward one candidate or the other by a comfortable margin.

Larry Sabato, a political expert at the University of Virginia, points out that "Forty of the 50 states are already decided. We can go right down today and tell you 40 of the 50 states.  This election is all about 10 states and less than ten-percent of the population."

Under the U.S. electoral system, each state has a certain number of electoral votes based on its population.  In all but two states (Nebraska and Maine), the candidate who wins the popular vote in a given state wins all of that state's electoral votes.  Out of a total of 538 electoral votes, it takes a minimum of 270 to win the presidency.

The electoral map suggests that sharp political divisions will remain, no matter who wins this year's election.

"It will be very hard for any one president to reduce those divisions," says Stephen Wayne, who has written about the history of U.S. elections at Georgetown University in Washington. "It has been a long time since we have had one party that has been a dominant party.  And as long as both parties are about equal, and as long as both candidates try to reach out to as many people as possible, these internal divisions will probably persist."

Following the disputed presidential election in Florida four-years ago, both parties have mounted aggressive drives to register millions of new voters to boost turnout.  In addition, 23 states authorized early voting periods to encourage people to get to the polls.

But both campaigns also have thousands of lawyers standing by in several states to bring legal challenges in the event of voting irregularities, once again raising the specter that a close election might not produce a clear winner on election night.