Mitt Romney is to fly to South Carolina for the next round of the Republican presidential race after cruising to victory in the New Hampshire primary.

Romney has managed a rare achievement for a non-incumbent candidate: winning the first two races, the New Hampshire primary and the Iowa caucuses.

The wins establish him as favourite to win the Republican nomination to take on Barack Obama for the White House in November.

But he will find deeply conservative South Carolina a tougher proposition than either Iowa or New Hampshire. South Carolina, where the politics are often brutal, has historically proved to be the crucible for Republican candidates.

Celebrating with supporters at a university campus on the outskirts of Manchester, Romney said: "Thank you, New Hampshire! Tonight, we made history."

He ignored his Republican rivals, behaving instead as if he was already the nominee and devoting his victory speech to criticising Barack Obama in a possible warm-up for the general election.

But Romney does not leave New Hampshire unscathed. His Republican rivals have done him damage by focusing on his record as chief executive at the Bain company, which they described as a coven of corporate raiders and vultures, taking over smaller firms and laying off workers.

In spite of Romney winning by a large margin, Obama's re-election team will be heartened by the relatively low turnout in New Hampshire, suggesting a lack of enthusiasm among Republicans for Romney and the other GOP candidates.

That view is reinforced by a strong second place for libertarian Texas congressman Ron Paul, who is out of step with mainstream Republicans, advocating a non-interventionist policy abroad and minimalist government at home.

Paul has, however, successfully tapped into a strong anti-war mood in the country in the wake of Iraq and Afghanistan, particularly among the young.

It was a good finish for a candidate who has for so long been on the margins of US politics. His campaign team does not expect to win the nomination, but he can keep the race going for months, building up a bloc of delegates to take to the Republican convention in Florida in August, where the nominee is formally chosen.

He told his cheering supporters he had phoned Romney to congratulate him on a clear-cut victory. "But there was another winner tonight. We had a victory for liberty," Paul said.

The biggest loser of the night was Rick Santorum, unable to capitalise on his late surge in Iowa just a week ago, which brought him to within eight votes of Romney. He suggested the New Hampshire result was a "temporary setback" and warned Romney that if he thought it would all be over after a few states, he would be disappointed. He belittled Romney's win, saying it had taken place in his backyard.

"On to South Carolina," Santorum said.

It was also a disappointment for Jon Huntsman, the former Utah governor who staked everything on New Hampshire and who needed at least a second-placed finish. In spite of a lack of money and organisation, he told his supporters he will take his campaign to South Carolina. "Ladies and gentlemen, I think we're in the hunt," he said. "I'd say third place is a ticket to ride."

It was a bad night for former House speaker Newt Gingrich. Furious over $3.5m in negative ads directed at him in Iowa by Romney supporters, he is out to exact revenge in South Carolina.

Texas governor Rick Perry, who opted out of competing in New Hampshire and instead focused on South Carolina, claimed he had a headstart in that state. As a southerner with vast election coffers, he may do better. Difficult for him to do worse, though.