She denies it at every turn. Democrats hope it's all bluff. So will Hillary run?

No, Hillary Clinton won't be in Durham, New Hampshire, tonight to participate in the latest of those instantly forgettable Democratic candidates' debates. Moreover, not a week passes without her disavowing all ambitions to run for the White House in 2004, and all logic would tend to support her. And yet the shade of Hillary refuses to go gently from the Presidential stage. Her admirers nurse a flicker of hope, her rivals-who-are-not must surely feel just a flicker of fire. Could not the seemingly impossible yet come to pass? And precedent suggests the door is not quite shut.

In US political lore, the denial against which all other political disclaimers must be measured is that of Lyndon B Johnson (LBJ) on 31 March 1968, when he took himself out of that November's election to devote himself to the search for peace in Vietnam. "Accordingly," he told a stunned nation that evening, "I shall not seek, and I will not accept, the nomination of my party for another term as your President." Now Hillary is fine on the Part One of the Johnson formulation. At this stage in proceedings, no one expects her to join an already over-crowded Democratic field for 2004 and, even if she wanted to, it is almost certainly too late. She has no organisation in place, and every sign right now is that the upstart outsider Howard Dean is cruising to victory. He is ahead in the polls in Iowa, and has overtaken the hapless Senator John Kerry to lead by a staggering 30 per cent in New Hampshire.

If the former Vermont governor wins these first two primary states, most political analysts believe that Dr Dean will be virtually unstoppable.

And, runs the conventional wisdom, why should Mrs Clinton bother? Assuming that the US economy continues to recover, and that US casualties in Iraq remain at their present politically tolerable level, George Bush must be a strong favourite for re-election. Far better to wait until 2008 when the race will be completely open. Now she can build up her credentials, get her own political machine in place and, subtly, remake her image.

Insofar as the persona ever existed, Hillary the rabid liberal and peacenik is no more. But, for her left-wing constituency, the legend lingers. Less noticed, she has moved to fill the national security gap in her resumé by joining the Senate Armed Services Committee, where she works hard, sometimes in alliance with Republicans, even with conservatives like South Carolina's freshman Senator Lindsey Graham (who, as a Congressman, was among the most fervent supporters of the impeachment of her husband).

Mrs Clinton voted for the war with Iraq in October 2002 and her recent well-publicised trip to Baghdad seems to have done nothing to have changed her mind. In that respect, she contrasts vividly with her Massachusetts colleague Mr Kerry, whose campaign is collapsing largely because of his failure to explain why he agreed with the war then, only to oppose Mr Bush's $87bn (£50.2bn) Iraq stabilisation package now.

Mrs Clinton can be as trenchantly critical of Republicans as anyone. But she is quietly metamorphosing into a Democratic moderate, whose appeal extends into the centre of the political spectrum. All seems geared to a White House bid in 2008. But her most impatient supporters have not lost heart.

What if the economy collapsed or Iraq degenerated into chaos, they wonder, suddenly giving the Democrats a real shot at victory next year? Mrs Clinton's White House ambitions are not in doubt. But if she sits 2004 out and Dr Dean, say, won, she would be unable to run in her own right until 2012, when she would be 65, older than any incoming President since Ronald Reagan. And even better, her fans have yet to hear Part Two of the LBJ disclaimer: what if the nomination was offered to her on a plate? Thus a fantasy circulates. Dr Dean does well in the primaries, but not as well as expected, and remains without a watertight majority of delegates as the Democratic convention opens in Boston on 26 July 2004. Amid continuing public doubts over the electability of the former Vermont governor, other candidates continue to jockey for the prize.

At which point enter Hillary as dea ex machina, a perfect compromise to resolve a deadlocked convention. Now it must be said that this political junkies' heaven has not materialised in half a century or more, and that it will be harder than ever to bypass candidates who have weathered an unprecedentedly gruelling primary season in favour of some-one who has not campaigned at all. But, her supporters would argue, the people's will would be respected if Hillary were to emerge as the anointed one.

For do not polls show that she is the first choice of more than 40 per cent of registered Democrats, three times the number who prefer Dr Dean? With the passing of Bill Clinton from the presidential scene, she is unquestionably the Democrats' brightest political star. She is their most potent fundraiser, while the stunning success of her memoirs, Living History, a turgid piece of political boilerplate if ever there was one, only confirms her popularity. When Mrs Clinton attends a candidates' event, she steals the show.

Small wonder then that her coquettish performance on no fewer than three Sunday political talk shows at the weekend, at which she laughed off all speculation for 2004, did not entirely convince everyone. Could not Mrs Clinton consciously be playing hard to get, positioning herself for her party as General de Gaulle once positioned himself for France, 'dans la reserve de la Republique?' Politics is a strange business. Few would have predicted eight months ago that, come December, a little known ex-governor of an obscure New England state would be the frontrunner for the Democratic nomination. Who now can be quite certain that eight months hence, a very well-known former-First Lady will not be in the running to receive it?

The candidates

HOWARD DEAN: Former governor of Vermont, and self-proclaimed outsider. Riding a wave of Democratic anger at President Bush, he embodies the grass-roots frustration at the failure of the party to provide a decent opposition. Best funded candidate and clear frontrunner.

WESLEY CLARK: The former Nato chief only entered the campaign race in September.

After some initial fumbles, he has performed competently but blandly. At or near the top of nationwide (i.e. not state) Democratic polls.

RICHARD GEPHARDT:

Candidate in 1988, he is staking all on victory in 19 January's Iowa caucuses, which he won 16 years ago. An old-fashioned 'machine' politician, seen by some as the most plausible 'Stop Dean' candidate in the field.

JOHN KERRY:

Once the favourite, but now the Senator from Massachusetts is floundering, unable to explain his about-turn on Iraq. He has shaken up his campaign staff, and is using his own resources.

JOHN EDWARDS:

Suave southerner in the Clinton mould, but failed to impress in Iowa and New Hampshire. Needs a win in South Carolina (next door to his native North Carolina) on 3 February to keep his

bid alive.

JOE LIEBERMAN:

As Al Gore's running mate in 2000, he had more recognition than rivals. But centrist policies and support for the Iraq war were a hard sell to activists. May be the first top-tier candidate to drop out.

DENNIS KUCINICH:

Represents Cleveland in Congress. An avowed liberal and opponent of

the Iraq war, he has called for the creation of a Department of Peace. He has no real chance of winning the nomination.

CAROL MOSELEY BRAUN:

The only woman in the race, she is a former Illinois Senator and US ambassador to New Zealand. Her chances of success are zero but she could prove a dangerous spoiler if the race gets close

THE REV AL SHARPTON:

A rank outsider with no relevant experience for high office. He is believed to be running mainly to win national recognition, and thus supplant the Rev Jesse Jackson as the pre-eminent black leader in the US