They’re both calling for a revolution against the banks, corporations and Washington lobbyists, but the front runners in the race for the White House couldn’t be more different. The 74-year old self-styled “democratic socialist”, Senator Bernie Sanders, is the most left wing victor of a presidential primary in living memory. He's also the first Jew in a country that has never had a Jewish president.

Donald Trump is a bellicose real estate billionaire, a Christian of no fixed denomination. He has never held elected office and is the first Republican frontrunner in decades to openly play the race card. They are both leading their parties by a country mile.

The party establishments are horrified and will try everything to halt the delinquents in their midsts. They might well succeed. But there's a real possibility that, come November, we could be seeing a US presidential contest between highly combative candidates of the far Left and the far Right.

Mr Sanders didn’t just defeat rival, Hillary Clinton; he crushed her by 22 percentage points, the biggest margin ever in a contested Democratic party primary. The race has barely begun, and no one is writing off the former secretary of state. But the matriarch of the Clinton clan is beginning to looking like yesterday's woman.

In New Hampshire, she couldn't even command the gender vote. An astonishing 82 per cent of women under 30 years of age voted for Bernie Sanders in the primary. In this conservative north-east state the former student radical defeated Mrs Clinton in all gender and ethnic groups under the age of 50 and earning less than $200,000.

Donald Trump won the New Hampshire Republican party primary by a similar margin, roaring back after his setback in Iowa and leaving his rivals looking like losers. “I love you all”, he cried in his victory address using the Trump catch phrase. He has also promised to bring back waterboarding “and much worse”. Tough love has never looked tougher.

Trump’s extraordinarily mobile mouth seems to morph into a sneering foghorn as he vows to make America strong by the biggest military build-up in history: “We are going to kick Isis's ass.” His economic policy is similarly Neanderthal: “We're going to beat China, Japan and Mexico at trade”, he says, “and all those countries that are taking so much of our money away from us.”

Mr Trump is a crude populist who makes Silvio Berlusconi look like a liberal technocrat. He wants to ban Muslim immigrants and build a wall at the Mexican border financed, he says, by the Mexican government. He breaks all the rules: he’s sexist, snubs the media (even conservative Fox News) and uses abusive language, even echoing a claim that fellow Republican candidate, Ted Cruz, is “a pussy”.

GOP grandees are appalled, but Mr Trump’s supporters love his brashness, especially the working class white men and women who attend his rallies. They feel threatened by immigration, get their politics from Clint Eastwood films and think their country has been on the losing side since 9/11.

Both Mr Sanders and Mr Trump claim to be “revolutionaries” leading “movements”. In a sense they are both right. They are insurgent populists expressing the anguish of the alienated and the dispossessed. They are miles apart politically, but united in their hostility to retail politics and their respective party machines.

They’ve both been written off by media pundits as no-hopers. Mr Sanders came top of Time magazine's Person of the Year reader’s poll last year but the snooty editors removed his name from the short list for their celebrated annual cover story. Even the godfather of American radicalism, Noam Chomsky, said Mr Sanders's chances of winning New Hampshire were “virtually nil” .

Mr Sanders is very like our own Jeremy Corbyn. He was similarly dismissed as a beardy, over-the-hill relic of 1970s Leftism. Mr Corbyn went on to win the Labour leadership by the biggest margin in Labour history and has transformed the party by attracting thousands of new supporters and members. His strength, like Mr Sanders's, is his appeal across the generations to people who want genuine social and political change.

Mr Sanders is a relentless critic of inequality and the “decline of the middle class”. He condemns a system in which, he claims, “the top 400 billionaires own as much a 150 million Americans”. This resonates with many young Americans experiencing job losses, falling wages, insecurity and student debt.

They see the rich gaining ever larger shares of national income and wealth, including the bankers, immortalised in the hit film The Big Short, who were bailed out by $700 billion of public money and returned to their old ways. Meanwhile, social security is being cut and new, post-recession jobs seem to be low paid and low grade.

Like Mr Corbyn, Mr Sanders isn't quite as Left-wing as he appears. He calls himself an independent but he mostly votes with the Democrat mainstream. He voted in support of military action against terrorists in Afghanistan, though he was a trenchant critic of the Iraq war. He wants fairer taxation, the break up of the big banks, free university tuition and a higher minimum wage. But he doesn’t want to nationalise business and says his economic inspiration comes from the former US President, Franklin D Roosevelt; nor is he a supporter of unilateral nuclear disarmament.

He supports what he calls a “minimum national deterrent”, something like 500 nuclear missiles against a US arsenal of around 1,500. And he has also voted several times against gun control bills, as Hillary Clinton never fails to remind him. She has also strongly hints that he is sexist.

But his youthful supporters don’t see it that way. In Iowa, the septuagenarian won the support of 84 per cent of voters aged under 29 They are too young to remember when “socialist” was synonymous with “communist”. For many young people today, being old looks quite cool. Witness the enduring popularity of people like Leonard Cohen, Neil Young, Bruce Springsteen, in their 70s or pushing it. Older people can convey an air of authenticity. They are unspun.

Like Nicola Sturgeon, another beneficiary of insurgent politics, Mr Sanders handles his own Twitter account. He has built on Barak Obama's success in raising huge sums from crowdfunding small donations, which means he doesn’t have to sell out to corporate donors.According to the New York Times, Sanders raised $26 million dollars in the last quarter of 2015 alone and is outspending Hillary Clinton.

America has always been a land of extremes and it has never been more so in its politics. Americans are angry and they want politicians who are angry too. It could be that they will soon have two presidential candidates who express both sides of this ire: the righteous social democracy of Mr Sanders versus the racial hyper-nationalism of Mr Trump. Americans may have to ask themselves, in the immortal words of Harlan County: which side are you on?