Photo AP
The Republican presidential hopeful now has three consecutive wins, after victories in New Hampshire and South Carolina.
Senators Marco Rubio and Ted Cruz, who have been attacking each other this week, are vying for second place.
GOP officials said they were looking into reports of double voting and not enough ballots at one caucus site.
Some volunteers also wore clothing in support of Donald Trump, but officials said this was not against the rules.
In his victory speech, Donald Trump told a roaring crowd of supporters: “We’re winning, winning, winning the country, and soon the country is going to start winning, winning, winning.”
Nevada, typically a swing state with a substantial Latino population, is crucial to the election process. Hillary Clinton won the state on February 20 in the Democratic race.
Some 30 delegates – around 1% of the total – are up for grabs in the Nevada caucuses, the first Republican test in the west of the United States.
Early results show Donald Trump has a 42% lead over the rest of the Republican pack, with his closest rival Marco Rubio getting 25% of the vote.
In the Democrats’ caucus in Nevada last week, Hillary Clinton beat rival Bernie Sanders by five percentage points.
On February 27, both candidates face each other in South Carolina, where they are focusing their campaigns on the black vote.
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