MANCHESTER, N.H. (AP) - Donald Trump will win at least 10 delegates in New Hampshire and John Kasich will win at least three. Ted Cruz and Jeb Bush will both win at least two, with six delegates still to be allocated.
In the overall race for delegates, Trump leads with 17, Cruz has 10, Marco Rubio has seven, Kasich has four and Bush has three.
It takes 1,237 delegates to win the Republican nomination.
Click here for full results from the New Hampshire primaries
A big victory for Donald Trump in New Hampshire, a big victory celebration for the billionaire businessman. He takes the top spot after second-place finishes in the Iowa caucuses.
Trump is basking in his victory in Tuesday's Republican presidential primary in New Hampshire and says that America under his leadership will "start winning again."
Trump is telling supporters that he'll be the "greatest jobs president God ever created."
He's promising that if he's commander in chief, he'll "knock the hell" out of the Islamic State group and negotiate what he says would be better trade deals.
A Trump presidency, he says, would mean "nobody is going to mess with us."
When word came just at 8 p.m. that Trump was declared the winner, his supporters at campaign headquarters in Manchester shouted his name and they waved foam fingers emblazoned with the phrase, "You're Hired."
Donald Trump says his campaign is $45 million under budget as he enters the second race of the presidential nomination process.
Speaking to MSNBC's Morning Joe as polls opened in New Hampshire Tuesday, Trump acknowledged that he's polled well in the Granite State but urged people to go out and vote.
Trump also addressed a possible third-party run by former New York City Mayor Michael Bloomberg, calling Bloomberg his friend, but acknowledging some of his shortfalls as mayor with regard to property development.
Trump has maintained a lead in most New Hampshire polls among his Republican contenders leading up to Tuesday's primary.
Donald Trump is also airing a new television ad that bashes Ted Cruz as "the worst kind of Washington insider."
The two candidates are after the same voters, people who want to shake up the federal government by electing an "outsider" president.
The 30-second spot that started airing Tuesday says Cruz of "talks from both side of his mouth" on allowing immigrants who are in the country illegally to stay, and took "sweetheart" loans from Wall Street banks when he ran for Senate in 2012. Then the narrator says Cruz's presidential campaign employed "dirty tricks" when it sent word to Iowans on the night of that state's caucuses that Ben Carson might be dropping out.
Cruz is "the worst kind of Washington insider, who just can't be trusted," the Trump ad concludes, showing Cruz's "TrusTED" campaign slogan.
Trump's latest commercial is part of a nearly $500,000 ad buy there.
South Carolina is the next state to vote in the GOP nomination fight, on Feb. 20.
Ohio Gov. John Kasich has finished second in New Hampshire's Republican presidential primary.
There's a tight race for third among Texas Sen. Ted Cruz, former Florida Gov. Jeb Bush and Florida Sen. Marco Rubio. It's still too close to call right now.
Kasich emerged from the pack of candidates to finish behind billionaire businessman Donald Trump on Tuesday night.
Kasich says the key to his second-place finish in New Hampshire's Republican presidential primary was that the "light overcame the darkness" of American politics.
The Ohio governor tells supporters that his positive campaign overcame negative attacks funded with tens of millions of dollars.
According to exit polling, John Kasich does best with voters looking for a candidate with political experience -- along with moderates, better educated voters and those who made their vote decision in the past few days.
Kasich's campaign manager says he expects an increased flow of contributions to the candidate's campaign after the strong showing.
In the tiny town of Dixville, which votes at midnight on primary day, Kasich sneaked past Donald Trump, 3-2, among Republicans.
Kasich's wife Karen joined him on the trail for the final hours of campaigning before the polls close.
Donald Trump may have captured the GOP presidential primary in New Hampshire and John Kasich came next, but Ted Cruz sees a different real winner of the contest.
The Texas senator -- who won the leadoff Iowa caucuses but is fighting for third in New Hampshire -- says it's the "conservative grassroots."
Cruz says he's proved the critics wrong for says a conservative couldn't do well in New Hampshire.
Now, he says he's focused on upcoming contests in South Carolina, Nevada and across the South in early March.
Ted Cruz says Donald Trump has no choice but to engage in profanity because the billionaire businessman can't defend his record.
A day earlier, Trump used a vulgar term for a coward to refer to Cruz, who briefly addressed the insult Tuesday afternoon as he greeted voters inside Manchester's Red Arrow Diner.
"Part of the reason that Donald engages in insults is because he can't discuss the substance. He can't defend his record. For example, a vote for Donald Trump is a vote for Obamacare," Cruz told reporters as he walked into the diner.
Trump has said that's a "lie." Cruz charges that Trump supports universal health care that could lead to health care rationing.
Cruz says, "Donald can't defend that. So instead, his approach is to engage in a profane insult. I'm not going to respond in kind."
Jeb Bush says New Hampshire voters have "reset" the Republican presidential race.
The former Florida governor -- who's in a fight for third place with Ted Cruz and Marco Rubio -- says he's campaign "is not dead" and that's he's looking forward to the upcoming contest in South Carolina.
Bush was betting big on New Hampshire to help him recover from his poor single-digit showing in the Iowa caucuses.
Jeb Bush is buoyed by some favorable poll numbers and growing crowds at his town halls. He's hammering away at front-runner Donald Trump and saying his own experience as a two-term Florida governor is a better presidential qualification.
Bush, appearing on Fox News Tuesday, says he's determined to knock down Trump because he says "this guy is not a conservative" and he cannot "win by insulting your way to the presidency."
Bush says he's the only candidate offering detailed plans to lift people out of poverty, raise middle class incomes and keep the country safe.
He says "that's what people want," not "the insults and all the divisiveness."
Marco Rubio says he's disappointed in his performance Tuesday in New Hampshire's Republican presidential primary, and he's blaming himself.
And the Florida senator -- who finished a surprising second in the leadoff Iowa caucuses -- says he has a good idea why he's in a fight for third place with Texas Sen. Ted Cruz and former Florida. Gov. Jeb Bush.
Rubio is pointing to his performance in the last debate before the primary.
He tells supporters: "I did not do well on Saturday night."
It seemed like a golden opportunity for Marco Rubio to convince a New Hampshire voter. But the Florida Senator couldn't seal the deal.
According to exit polling, Marco Rubio does best among voters for whom experience and electability is important.
Rubio and Derry Republican voter Stephanie Tespas stood outside a middle school locked in a quiet and serious conversation about cancer.
Tespas told Rubio of her son's genetic condition, the same as her husband who battled and survived cancer. Rubio nodded and mentioned his own father's losing battle with lung cancer after a lifetime of smoking.
After Rubio thanks Tespas and got into his SUV, she said she remained undecided about who to support as she walked into the school to vote.
Tespas left the gymnasium without saying who she supported, except that it wasn't Rubio.
"I just don't think he's quite ready," she said. "I wanted him to be more personal. I felt like I was in one of his commercials."
An outside group that's helping Republican presidential candidate Marco Rubio is spending more than $1.5 million on digital and media advertisements in South Carolina and Nevada -- the next states on the 2016 election calendar.
The new expenditures are by Conservative Solutions PAC, a super political action committee that faces no contribution limits.
All but about $200,000 is for South Carolina. That's according to reports filed with the Federal Election Commission.
Conservative Solutions is the second-most-active super PAC in the presidential race so far. Only Right to Rise, which is boosting Republican Jeb Bush, has spent more on television and radio.
Chris Christie is telling his campaign volunteers to work now, celebrate later.
Visiting his Bedford headquarters, Christie says the Republican contest is far from over, and that the campaign has much work to do to get voters to the polls.
Christie continued to tout his performance in Saturday's debate, during which he came down hard on Florida Sen. Marco Rubio, saying it solidified the central premise of his campaign: that his work and life experience make him the best prepared to take on Hillary Clinton and win the presidency. And he says he's fine with others criticizing his record, because at least he has one.
She's back in the pack among Republicans in New Hampshire, but the fight isn't going out of Carly Fiorina.
The Republican presidential candidate tells supporters at a country club in Manchester that "I'm not going to sit down and be quiet, and neither are you."
She's taken the stage with her husband, Frank, by her side. And what's playing in the background? "I Won't Back Down," by rocker Tom Petty.