Mrs Clinton and Mr Trump cast their ballots in New York polling stations, alongside their spouses.

High turnout is being reported across the country with polling stations due to begin closing on the East Coast at 19:00 EST (24:00 GMT).

Mr Trump has again declined to say whether he will accept the results.

"We're going to see how things play out," the Republican candidate told Fox News on Tuesday, while alleging there had been voting irregularities. "I want to see everything honest."

Some polling locations have reported equipment failures and long lines, but they appeared to be routine problems.

Mr Trump filed a suit against the Clark County Registrar of Voters in Nevada, accusing the state of keeping early voting stations open longer than the designated closing time.

But a judge rejected the request, citing concerns about revealing the identities of poll workers.

The Manhattan real estate mogul's lawyers had asked for relevant early ballots not to be mixed with other ballots.

Polling in Nevada shows the race between Mr Trump and his Democratic rival, Hillary Clinton, is extremely tight.

Mrs Clinton voted at her local polling station in Chappaqua, New York, with her husband, former President Bill Clinton, at her side.

The former Secretary of State told reporters: "I know how much responsibility goes with this.

"So many people are counting on the outcome of this election, what it means for our country, and I will do the very best I can if I'm fortunate enough to win today."

Results are expected some time after 23:00 EST (04:00 GMT on Wednesday) once voting ends on the West Coast.

State projections will not be available until polling ends - in most states between 19:00 EST (24:00 GMT) and 20:00 EST (01:00 GMT).

There are signs of a high turnout among Hispanic voters, which is believed to favour Mrs Clinton.

Mr Trump was expected to attract support mainly from white voters without college degrees.

Financial markets and betting exchanges have largely predicted a Clinton win.

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