HILLARY Clinton has captured Nevada’s Democratic caucuses and Donald Trump has won South Carolina’s Republican primary as Jeb Bush bows out of the race.

Hillary Clinton overcame an unexpectedly strong surge by Bernie Sanders and potentially eased the anxiety of some of her supporters.

Clinton won the backing of voters who said electability and experience were important in their vote. But in a continuing sign of her vulnerability, Sanders did best with voters looking for a candidate who is caring and honest.

The polling of voters was conducted for The Associated Press and the television networks by Edison Research as voters arrived at 25 randomly selected caucus sites.

She capitalised on a more diverse Democratic electorate who helped her rebound after a second-place finish to Sanders in the New Hampshire primary.

“Some may have doubted us, but we never doubted each other,” Clinton told her cheering supporters during a victory rally in Las Vegas. “This one is for you.” She said Americans are “right to be angry,” but are also hungry for “real solutions.” Sanders said in a statement that he’d congratulated Clinton on her victory, but then declared his campaign has “the wind at our backs as we head toward Super Tuesday” — the multistate voting contests on March 1.

Clinton’s victory in Nevada could be vital in holding off a challenge from Sanders that has been tougher than almost anyone expected. Clinton narrowly won the lead-off caucuses in the Midwestern state of Iowa, but the Vermont senator had a runaway victory in the tiny northeastern state of New Hampshire. Clinton now leads in delegates pledged to her at the Democratic Party’s national convention in July, but only has a fraction of the number needed to secure the nomination.

For Democrats, the contest between Clinton and Sanders had grown closer than expected.

Sanders, a self-proclaimed democratic socialist, had energised voters, particularly young people, with his impassioned calls for breaking up Wall Street banks and providing free tuition at public colleges and universities.

But Clinton prevailed in Nevada with the backing of women, union workers, minorities, moderates and voters who are certain that the former secretary of state will have a better shot at winning in November, according to entrance polls. Sanders won three-fourths of voters 45 and under, but Clinton offset that by picking up two-thirds of voters over 45.

A large majority of blacks supported Clinton, an outcome that bodes well for Clinton in upcoming southern state primaries. Hispanics were relatively closely divided between the two candidates.

Clinton’s win means she will pick up at least 18 of Nevada’s 35 delegates.

TRUMP WINS SOUTH CAROLINA

Donald Trump has won the South Carolina Republican primary, a second-straight victory for the billionaire real estate mogul after his first-place finish in New Hampshire.

Trump’s supporters erupted into cheers as they learned their candidate had won South Carolina’s GOP primary.

Supporters gave each other high-fives and held Trump signs high above their heads as they celebrated. Some chanted “USA! USA!” Hundreds of people are gathered in a ballroom at the Spartanburg Marriott for Trump’s watch party, where they’re snacking on cubed cheese and crudit, and sipping beers from plastic cups.

Trump is expected to deliver a victory speech soon.

Texas Senator Ted Cruz and Florida Senator Marco Rubio are in a close race for second.

No candidate has shaken the establishment more than Trump. The billionaire businessman spent the week threatening one rival with a lawsuit, accusing former President George W. Bush of lying, and even tangling with Pope Francis on immigration.

The prospect of a Trump win alarmed rival Jeb Bush, the former Florida governor trying mightily for a strong showing in the first southern state to vote.

“Trump can’t win, plain and simple,” Bush told reporters outside a polling place in Greenville, South Carolina. “This isn’t about appealing to people’s deep anxiety ... He can’t be president. A ton of people would be very uncomfortable with his divisive language and with his inexperience in so many ways.”

Neither Bush nor Rubio expected to win South Carolina. But they wanted to finish ahead of one another; otherwise, there would be tough questions about long-term viability.

JEB BOWS OUT

Republican Jeb Bush has ended his campaign for the US presidency after a disappointing finish in South Carolina.

The former Florida governor and political scion told supporters that he’d tried to stay true to what he believes.

Still, he was lagging far behind in the primary in South Carolina, where his well-organised campaign was outmatched by insurgent billionaire Donald Trump, and Senators Ted Cruz and Marco Rubio.

“I’m proud of the campaign that we’ve run to unify our country and to advocate conservative solutions,” a visibly emotional Bush said.

“The presidency is bigger than any one person. It’s certainly bigger than any one candidate.” “I firmly believe the American people must entrust this office to someone who understands that whoever holds it is a servant not the master,” Bush said.

The son of George HW Bush and brother of George W Bush entered the race to huge expectations in June, and quickly fuelled them with fundraising.

Bush and his allies raised more than $US150 million ($A210 million) by the end of 2015 — far more than any of his Republican rivals.

However, Bush’s presence in the race and fundraising potential wasn’t enough to dissuade more than a dozen other Republicans from entering the race, including fellow Floridian, Senator Marco Rubio. Bush’s failure to ignite was not simply a factor of the size of the Republican field.

Bush, like others, was caught off-guard by the durable popularity of political outsiders - particularly Trump.

Bush took shots at Trump’s lack of experience while Trump attacked Bush’s family legacy, particularly the unpopular Iraq war waged by his brother George W Bush.

Bush went on to finish sixth in the Iowa caucuses, but barely squeezed ahead of Rubio in New Hampshire for a fourth place finish. South Carolina was viewed as a last early voting state for Bush to make a mark.

Having previously kept his family at arm’s length, Bush brought all family ties to the forefront ahead of South Carolina.

His father and brother both won the South Carolina primary when they were seeking the presidency, and he had set his hopes high there for a campaign revival.