US election 2016: New York primaries crucial for Clinton and Trump
New York is holding presidential primaries seen as key for both Republican and Democratic front-runners after their recent defeats.
Democratic hopeful Hillary Clinton, a former senator for New York, is expected to win against Brooklyn-born Vermont Senator Bernie Sanders.
For the Republicans, Queens-born Donald Trump is likely to come ahead of Texas Senator Ted Cruz.
Wins will put Mrs Clinton and Mr Trump closer to securing their nominations.
As Mr Trump cast his votes at Central Synagogue in Manhattan on Tuesday morning, he said: "It's just an honour, and my whole reason for doing this is to make America great again."
Mrs Clinton voted with her husband, former President Bill Clinton, near their home in upstate Chappaqua.
They hope big victories in the delegate-rich state will help them regain momentum and overcome criticism over the strength of their campaigns.
It has been a fierce campaign in the state, with the leading candidates using their local ties to attract voters.
Hillary Clinton was twice elected senator for New York, and a defeat there would be a devastating political blow.
Whereas Mr Trump, who was born in the New York City borough of Queens, lives in a building bearing his name in midtown Manhattan.
The primaries are the state's most decisive in decades in selecting the candidates, and polls will be open until 21:00 (01:00 GMT Wednesday)
Mrs Clinton's side sees the vote as a make-or-break moment, and they say a victory there will virtually seal her Democratic nomination.
Opinion polls have given her a lead over Mr Sanders, who has won seven out of the last eight state votes.
"We are not taking anything for granted,'' Mrs Clinton said. "Tell your friends and your family, everyone, to please vote tomorrow [Tuesday]."
Mr Sanders hopes a victory in New York will keep his candidacy alive, as there are 291 delegates at stake.
The Democratic campaign has turned increasingly negative, with both candidates trading barbs about their qualifications.
On the eve of the primary, Mr Sanders accused Hillary Clinton of campaign finance violations, an allegation her team denied.
For Mr Trump, a win in New York will reduce the chances of a contested nomination at the Republican party convention in July.
The big question is whether he will make a clean sweep of all 95 Republican delegates at stake in New York by earning the majority of votes.
Polls have given him a clear lead over Ohio Governor John Kasich and Mr Cruz.
The Texas senator has had a poor performance in New York following an earlier comment in which he accused Mr Trump of having "New York values".
Mr Cruz made a few television appearances on Monday defending his remarks, but was already eyeing voters in Pennsylvania, which votes next week.
In a campaign event in Buffalo, Mr Trump told his supporters that "no New Yorker" could vote for Mr Cruz, who did "not represent what we need.''
But he made a slip-of-the-tongue during a speech about the 11 September 2001 attacks, when he erroneously mentioned the name of a popular convenience store chain.
"It's very close to my heart because I was down there, and I watched our police and our firemen down at 7/11, down at the World Trade Center right after it came down, and I saw the greatest people I've ever seen in action," Mr Trump said.
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