In New Jersey and Virginia, voters will pick governors.
New York City is choosing a successor to three-term Mayor Michael Bloomberg, a Republican-turned-independent.
Tuesday’s races are seen as an early test of the Republican and Democratic parties’ strengths ahead of next year’s critical congressional elections.
In New York City, Democratic mayoral candidate Bill de Blasio has taken a commanding lead in opinion polls over Republican Joe Lhota, a former senior official in the mayoral administrations of Michael Bloomberg and his predecessor Rudolph Giuliani.
Bill de Blasio, the city’s public advocate, ran Hillary Clinton’s 2000 Senate campaign. He is seen as one of the most liberal mayoral candidates in decades.
Under Michael Bloomberg, Joe Lhota ran the city’s public transport authority. He was lauded for quickly getting the vast subway system running again after a huge storm Sandy flooded swathes of the city last year.
In New Jersey, incumbent Republican Governor Chris Christie is expected to win re-election handily.
His Democratic challenger, state Senator Barbara Buono, has struggled to gain traction.
Analysts say Chris Christie’s popularity with voters in Democratic-leaning New Jersey makes him a contender for the 2016 Republican presidential nomination, because it could enable him to claim broad political appeal.
Chris Christie, 51, was already a popular figure when Sandy devastated the state’s coastline a year ago. His response to the storm attracted national attention.
He has been campaigning across the state since last week, even as polls suggested he had an advantage of at least 20 points on Barbara Buono.
While many in New Jersey support her positions, she has had difficulty raising money, even from Democrats, because of her relatively low profile.
The Virginia governor race pits Democrat Terry McAuliffe against Republican Ken Cuccinelli.
Terry McAuliffe is a businessman and veteran Democratic party fundraiser. He has close ties to former President Bill Clinton and Hillary Clinton, serving as chairman of her 2008 presidential campaign.
Ken Cuccinelli, the Virginia attorney general, has angled for the support of the hardcore conservative Tea Party movement of Republicans.
Terry McAuliffe, who has raised much more money, has sought to link Ken Cuccinelli to last month’s partial shutdown of the federal government, which was brought about by Republicans in Washington DC.
Virginia, long a Republican stronghold, has seen a demographic shift in recent years. Barack Obama, a Democrat, won the state in the last two presidential elections.
The results of Tuesday’s polls could prove an early measure of the parties’ support ahead of the midterm elections of 2014, which will decide the make-up of the House of Representatives, one-third of the Senate, and the governorships in more than half the states.
In Washington, Barack Obama’s Democratic party controls the Senate, while the Republicans hold sway in the House of Representatives.
Now in his second term, Barack Obama will vacate the presidency in 2017.
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