He is the son of a Nazi police chief who once declared his love for the noted UN secretary general and war criminal, Kurt Waldheim, and who still talks as if he has just arrived on Austrian Airlines. His rise to fame owes more to steroids than charm, and he is best known for impersonating a robot. Meanwhile, his crude remarks about women have not helped him counter persistent allegations of groping.

It is not the most promising record on which to build your first campaign for American public office, but the fact is that Arnold Schwarzenegger has every chance of being elected governor of California on October 7.

That says something about the pervasive mood of desperation in the Golden State these days, as it faces rapidly deteriorating public services, national ridicule and a $38bn deficit. Californians are so angry they are about to vote on whether to fire the governor they elected last year, the hapless, lacklustre and aptly named Gray Davis.

But the prospect of "The Governator" taking power in Sacramento says more about the extraordinary willpower of Schwarzenegger himself. Willpower that has propelled him along the winding road from the remote village of Thal amid the poverty and humiliation of a defeated country just two years after the second world war to the brink of political office in the US.

Wendy Leigh, Schwarzenegger's unauthorised biographer, went to Austria to research his roots, and came away convinced he plotted his political rise from an early age, using body-building and films as stepping stones to escape from a depressing home. There was certainly a lot to escape from. His father, Gustav, a frequently drunk local police chief who had signed up for the Nazi party after the 1938 Anschluss, apparently made no secret of his preference for the elder, more strapping of his two sons, Meinhardt.

Leigh portrays Schwarzenegger as obsessed with the pursuit of power and at one point quotes him as saying: "I wanted to be part of the small percentage of people who were leaders, not the large mass of followers. I think it is because I saw leaders use 100% of their potential... I was always fascinated by people in control of other people."

It would, of course, not be the first time the son of an unpleasant minor official from provincial Austria rose to high office through sheer force of will. But Arnold Alois Schwarzenegger is no Adolf Hitler, whatever you might have thought of Conan the Barbarian.

For one thing, he is quite liberal as far as Republicans go. He supports abortion rights and gun controls, and said the impeachment of President Clinton made him "ashamed to be a Republican".

Furthermore, Schwarzenegger could never rise to the top office in the land, as the constitution precludes those born outside the US from becoming president. Then again, all it would take is a constitutional amendment, and if Arnie did a good job in California...

But first Schwarzenegger has to win the governorship, and that will not be easy. Ronald Reagan did it, of course, but only after spending years working his way up the Republican party ranks. And Reagan was not carrying all Schwarzenegger's foreign baggage.

Possibly with a political future in mind, Schwarzenegger has done all he can to cauterise the wound left by his father. He commissioned the Simon Wiesenthal Centre to research his wartime record, and it came up with no evidence of atrocities.

Nevertheless, the star made amends for Gustav Schwarzenegger's political judgment by making generous and regular contributions to the Wiesenthal Centre, which presented him with a national leadership award for his humanitarian work.

"Every time he does a movie, he writes a cheque," Rabbi Marvin Hier, the centre's founder, said recently, pointing out that "Arnold is not his father." However, although his father may not have been a war criminal, Schwarzenegger sought out a fellow countryman who was. He invited Kurt Waldheim to be guest of honour at his 1986 wedding, at a time when the former UN secretary general's SS past was coming to the surface.

Schwarzenegger even made a point of mentioning him in his wedding speech, telling his guests: "My friends don't want me to mention Kurt's name because of the recent Nazi stuff - but I love him."

However, Rabbi Hier has also absolved him of that surprising declaration of affection, arguing that the actor probably did not know the extent of Waldheim's responsibility for atrocities in the Balkans.

As if SS links were not enough, there are the twinned issues of drugs and sex. Schwarzenegger has admitted using steroids to boost his muscle bulk while he was building himself up for his Mr Universe titles and his breakthrough film Pumping Iron. In that film he also appears to be smoking a spliff.

In fact, neither of those transgressions are likely to be too much of a barrier in California. But the sex issue might be tougher. This is not necessarily because of the allegations of groping, which were never proven, but of the offensive remarks to issue from his own mouth.

Back in 1988, he told Playboy he would never allow his wife or mother to wear trousers when they were seen with him on the grounds that dresses are more feminine. That was back in 1988, of course, but he does not seem to have mellowed. This is from an interview in last month's Esquire magazine on the subject of blondes and brains:

"As much as when you see a blonde with great tits and a great ass, you say to yourself, 'Hey, she must be stupid or must have nothing else to offer', which maybe is the case many times. But then again there is the one that is as smart as her breasts look, great as her face looks, beautiful as her whole body looks gorgeous, you know, so people are shocked." Not as shocked, perhaps, as California's women voters will be when they hear that particular quote, as surely they will. Davis's political rottweiler and California's answer to Alastair Campbell, Garry South, is already hard at work making sure that all the dirt on Schwarzenegger gets into the public domain early and often.

Two years ago, the last time Schwarzenegger was considering a run for the governor's mansion, South gave him a taste of what a real fight might look like when there are no stunt doubles to take the fall. He faxed political reporters a copy of a highly unflattering magazine piece on the Terminator star which referred to allegations of womanising, touching women inappropriately and his past behaviour as a body-builder. He attached a helpful covering note: "Here is the long-awaited Premiere magazine exposé on might-be gubernatorial wannabe AH-nuhld Schwarzenegger... the piece lays out a real 'touching' story - if you get what I mean."

People did. Although friends of Schwarzenegger in the film world went public in his defence and attested to his moral decency, the faxes were seen as a warning shot of what might happen if he decided he wanted to mix it with the big boys. Davis, who is unpopular and uncharismatic, is nonetheless respected for two things: his ability to raise money for his races and his dirty-tricks campaigns. Schwarzenegger, already committed to promoting Terminator 3, backed off from running against him last November, and pundits wondered if that was the last that would be heard of him on the political stage.

But, as the Schwarzenegger-as-android figure has so often promised us, he's back. And this time, he is much better positioned for the final assault on the governor's house in Sacramento. California is angrier and ready for an outsider to run against politics-as-usual. The rules of the recall vote mean that he does not have to compete in a primary, and so does not have to convince Republican activists, who might not appreciate his liberal position on social issues and his marriage to John F Kennedy's niece Maria Shriver.

Instead, that record will help sell him as a centrist and bring over floating voters. The last Republican to be elected governor in California, Pete Wilson, took the same liberal stance on abortion and guns. A 30-strong team of political fixers who used to work for Wilson are now running the Schwarzenegger campaign.

They ran what many saw as a dry-run campaign in 2002, promoting an initiative called proposition 49, which designated money for after-school programmes aimed at keeping young people out of trouble. It was not a very controversial measure - California has a major gang problem, with children as young as 13 involved - and it passed easily.

Schwarzenegger presented the case eloquently, however, and celebrated its victory at a project in the Latino area of east Los Angeles. He clearly relished the adulation of the crowds gathered there for the results, who encouraged him to seek higher office. He has already started wooing the Latino vote in the state, although it may require more than a few "hasta la vistas" to pluck them from their traditional Democratic party allegiance.

As well as starting out with name recognition that most politicians spend a lifetime trying to accrue, Schwarzenegger has another attribute essential to political success: money. He made $30m for his role in Terminator 3, just about what a high-octane governorship campaign costs. And that is just the proceeds from one film. Schwarzenegger has a business empire, including shopping malls a Boeing 747 and large chunks of Santa Monica.

Declaring his candidacy on the Jay Leno show on Wednesday night, he managed to present his personal fortune as a guarantee that he would take the side of the man in the street. He had so much money that he would not have to go cap in hand to the "special interests".

"The biggest problem we have is that California is being run now by special interests," Schwarzenegger declared. "We have to stop that."

In the wake of his Jay Leno appearance, he is ahead in the polls in a crowded field that includes the self-styled "smut peddler who cares", the Hustler publisher Larry Flynt, half a dozen minor celebrities and more than 400 other aspiring Californians.

But Schwarzenegger, like his metallic alter-ego, has been known to self-destruct, and anyone who has seen The Last Action Hero or visited a Planet Hollywood (which he started with Sylvester Stallone and Bruce Willis) knows that he is not invincible. But Stallone and Willis are yesterday's action heroes. Schwarzenegger is still going strong, fulfilling his plan.

It is a plan that he once chillingly spelled out to Playboy: "You have to create a need for yourself, build yourself up. While their empire goes on, slowly, without realising it, build your own little fortress. And all of a sudden it's too late for them to do anything about it."

The Arnie file

Arnold on his political ambitions

"I would rather be governor of California than own Austria."

On what makes Arnie run

"My political ambitions have nothing to do with vanity or the desire for power. I want to help people. I owe them something after all they've done for me."

On his physical credentials, in a recent Vanity Fair questionnaire

"Let's just say that Milton Berle had the same problem. What can I say? It's a curse."

On what type of boss he is

"I don't take any shit. I have to be a bit of a five-star general. I have no time for slacking off or failure. If you want to be part of the team, then you have to go and kick butt. If you don't like that kind of pressure then get the hell out."

On why he loves the holidays

"I love Thanksgiving. It's the only time in Los Angeles that you see natural breasts."

On the root of all evil

"Money doesn't make you happy. I now have $50m, but I was just as happy when I had $48m."

On his exercise regime, in 1979

"Having a pump is like having great sex. I train two, sometimes three times a day. Each time I get a pump, it's great. I feel like I'm coming all day."

Arnold in the movies

"I'll be back" (his catchphrase, from Terminator 2: Judgement Day)

"Hasta la vista, baby" (again, from T2)

"You're not sendink me to the cooler" (as Mr Freeze, in Batman and Robin)

"Please God, gimme strength" (appealing to the Almighty, in his flop thriller End of Days)

What others say about Arnold

"Arnold Schwarzenegger looks like a condom full of walnuts" - Clive James

"Arnold Schwarzenegger's acted in plenty of movies but spoken less dialogue than any actor, except maybe Lassie" - Robin Williams

"I've known Arnold for a long time and hold him in the highest esteem. Arnold is a perfect gentleman and a devoted family man" - True Lies star Jamie Lee Curtis, defending him against a Premiere magazine article which depicted him as a rapacious womaniser with a habit of harassing female crew members

"I think he's a leader. I think he has the ability to distil the essence of complicated issues and is very sort of solution-oriented" - Kindergarten Cop director Ivan Reitman, responding to Arnie's announcement

"This is the greatest thing to happen to comedy writers since Gerald Ford tripped on something" - US film critic Leonard Maltin

Xan Brooks