The surprise results from New Hampshire have thrown the US presidential race open to the challengers to the respective party establishments, but the odds are still stacked against them.

John McCain may have shocked his opponent Governor George W. Bush of Texas by the size of his victory (49 per cent to 30 per cent), but the next Republican primary in South Carolina on February 19th will be a tougher test for the senator from Arizona when he is faced with the full might of the well-funded Bush machine in a southern state.

Former New Jersey senator Mr Bill Bradley gave Vice-President Al Gore a fright as he almost closed the gap between them on polling day, but this has only sharpened the Gore campaign's determination to learn from its mistakes. The largely white, liberal-leaning, well-educated New Hampshire Democrats were an ideal campaigning ground for Mr Bradley, but he will face tougher challenges in the larger states where Mr Gore's trade union and African-American support will be important.

Some previous winners in New Hampshire such as Mr Pat Buchanan in 1996 and Mr Gary Hart in 1984 have quickly faded later in the campaigns.

But what New Hampshire has shown this week is that Mr Gore and Mr Bush can be beaten in spite of being the anointed candidates of their party establishments. Six months ago, Mr Gore barely deigned to acknowledge that Mr Bradley was challenging him for the Democratic nomination. He assumed he would be the Democratic candidate as did most of the party members of Congress, governors and office-holders.

Six months ago, Mr Bush was piling up millions of dollars and endorsements from the Republican establishment without hardly having to stir outside the state-house in Texas. Opinion polls showed him trouncing Mr Gore in a presidential election.

As for rivals for the Republican nomination, none of them seemed a serious challenge to the son of the former President. Mrs Elizabeth Dole trailed far behind as the number two choice. Mr McCain was somewhere in single digits and laughed off as a maverick who was fighting for the reform of the campaign finance system which gets most Republicans elected.

Then came New Hampshire. The small north-eastern state with only 1.2 million mostly white people with no income tax and the slogan "Live free or die", is often derided as an aberration in the American electoral process because it is so unrepresentative of the population as a whole. Yet, because it is by tradition the first primary election, candidates for their party nominations are forced to spend months campaigning there under a media spotlight while far bigger states are virtually ignored.

But such intensive campaigning does show up weaknesses as well as strengths as the candidates tramp through the January snows and address innumerable town hall meetings. It is not just the residents of New Hampshire who are getting a close look but the whole country, thanks to the media blitz which was bigger than ever this year.

The results in the Republican primary were a big shock for Mr Bush, who had not bothered to show up for the first debates with his rivals last October. The exit polls show almost every category of voter rejected him in favour of Mr McCain - men and women, rich and poor, graduates and non-graduates, liberals, moderates and conservatives.

Among the conservatives, Mr McCain was ahead by only one point, but this was surprising because the former prisoner and war hero had deliberately challenged Republican conservatives by his crusade to clean up election financing and by calling for a smaller tax cut than Mr Bush.

A peculiarity of New Hampshire greatly helped the McCain campaign. Not only has it a preponderance of registered independent voters, but they are allowed to vote in either the Republican or Democratic primaries. Most of them switched to Mr McCain, attracted by his dynamic, freewheeling campaign style in which he denounced Washington corruption and spinning as "lying".

Mr Gore and Mr Bradley also campaigned hard for the floating independent vote which three months ago was piling up for the former senator in the opinion polls. But Mr Bradley peaked too soon and he underestimated Mr Gore's street-fighting abilities and determination to do almost anything to win.

Mr Bradley's lofty, above-the-fray approach backfired badly in the Iowa caucuses as Mr Gore hammered his proposals for reform of the health system as disastrous for pensioners. Furious at what he called Mr Gore's "misrepresentation" of his policies, Mr Bradley began to hit back at Mr Gore's past fund-raising abuses - including the infamous Buddhist temple episode - and his swerves on the abortion issue.

This nearly worked and Mr Bradley won 48 per cent to Mr Gore's 52 per cent after trailing by 16 points in some polls just a week before. While a win is a win, Mr Gore must feel some apprehension that Mr Bradley is now energised to take the fight to him in the 28 Democratic primaries between now and the end of March.

Unlike Mr McCain, Mr Bradley has a large war chest at his disposal to pay for the TV ads in vital states such as New York and California. The Democrat establishment would have loved to see Mr Bradley crushed in New Hampshire so that he could fade away and leave the field clear to Mr Gore, who is running short of funds.

Instead, the contest between the two men is likely to get more venomous in spite of disclaimers from both campaigns. Appeals from Democratic congressional leaders to Mr Bradley to tone down his attacks on Mr Gore lest they give ammunition to the Republicans in the presidential campaign proper are ingenuous, given Mr Gore's distortions of the Bradley policies, but they reveal Democratic fears.

The pundits still believe Mr Gore and Mr Bush will be squaring off in the presidential campaign when it begins in September. But they are also hedging their bets.