Neo-Nazi activity in Austria is monitored by Vienna's Documentation Centre of Austrian Resistance (DÖW), an organisation founded in 1963 by former resistance fighters. Drawing two circles on a piece of paper to explain, researcher Heribert Schiedel talked about the rise of the far right in Austria.
"In the circle on the left you have legal parties such as the FPÖ. In the circle on the right you have illegal groups such as Blood and Honour. Two distinct groupings who pretend they are separate." He drew another circle linking the two.
"This circle links the legal and illegal," he says. "This signifies the Burschenschaften, right-wing brotherhoods founded in German universities. They have been long been associated with fascism and have a history of terrorism. Adolf Eichmann, Rudolf Hess and Heinrich Himmler were members of Burschenschaften - as are prominent members of the FPÖ in parliament.
"Neo-Nazis around the world are now looking to Austria for their lead because of the election result. The neo-Nazis believe their time is coming again. There is a new European right and its core is right here in Austria."
The Burschenschaften were banned by the allies after the second world war but reformed in the 1950s. In 1987, Olympia, one of the most extreme fraternities, nominated Rudolf Hess for the Nobel Peace Prize and it was Olympia who invited the controversial British historian David Irving to Austria in 2005 when he was arrested for denying the Holocaust.
Senior members of the FPÖ are "Burschenschafter", including Strache and Martin Graf, who was elected deputy president of the Austrian Parliament after the election. Ahead of his selection, Vienna's concentration camp survivors wrote to MPs asking them not to vote for him, but 70% of parliament backed him. The move caused outcry and was condemned by, among others, Dr Efraim Zuroff, from the Simon Wiesenthal Centre in Jerusalem. He said: "Our concern stems from the well-known ties Graf has with extreme right groups like the Olympia student union."
The FPÖ's Andreas Mölzer is also a member of the Burschenschaften and has been trying to create a far-right European block ahead of June elections to the European Parliament. Mölzer, an MEP, paid a clandestine visit to London last year to meet the BNP leader Nick Griffin.
Graf, Strache and Mölzer have always strenuously denied having any links to far-right extremist groups and the FPÖ says it only wishes to revoke the Verbotsgesetz because it believes in freedom of expression. Strache told Sunday Herald: "I have very often distanced myself from National Socialism, fascism and any other totalitarian ideologies." Graf said he "deplored" racism and anti-Semitism.
But as with Waldheim and Haider before, Strache has been at the centre of controversy and pictures surfaced last year showing the FPÖ leader wearing army fatigues and clutching what appeared to be a gun in a forest. The images of him were allegedly taken at a neo-Nazi training camp in his youth. Strache denied this and said the images were from a day out paintballing.
There was also a furore over a photograph of him giving a three-fingered salute - claimed to be a secret sign for far right extremists - but Strache dismissed this saying he was ordering beers in a bar. He is now referred to as "three beers Strache" by many Austrians.
The FPÖ has tried to distance itself from extremism recently but the party was founded by two former SS officers, Anton Reinthaller and Herbert Schweiger. Schweiger is still politically active and I met him at his Austrian home a few weeks before he was due in court charged with promoting neo-Nazi ideology.
Still remarkably sharp-minded, Schweiger was a lieutenant in the Waffen SS Panzer Division Leibstandarte Adolf Hitler, an elite unit originally formed before the second world war to act as the Führer's personal bodyguards.
It will be the fifth time Schweiger has stood trial for breaking the Verbotsgesetz law. He has been found guilty twice and acquitted twice and it quickly became apparent that little had changed in his mindset since his Third Reich days.
"The Jew on Wall Street is responsible for the world's current economic crisis. It is the same now as in 1929 when 90% of money was in the hands of the Jew. Hitler had the right solutions then," he said.
Schweiger - described to me as the "Puppet Master" of the far right - is a legendary figure for neo-Nazis across the world and he claimed the far right would soon have another leader like Hitler. If Schweiger was a senile old Nazi it might be possible to dismiss him as a harmless old man. But Schweiger remains a powerful man. His raison d'être is politics. He was a founding member of three political parties in Austria - the VDU, the banned NDP and the FPÖ - and he has given his support to the current leader of the FPÖ.
"Strache is doing the right thing by fighting the foreigner," he said.
As a "politician", Schweiger is of the school that believes the bullet and the ballot box go hand in hand. This belief goes back to at least 1961, when he helped to train a terrorist movement fighting for the reunification of Austria and South Tyrol, now part of Italy.
"I was an explosives expert in the SS so I trained the Burschenschaften how to make bombs. We used the hotel my wife and I owned as a training camp," he said. The hotel he refers to is 50 yards from his home.
Thirty people in Italy were murdered during the campaign. One man convicted for the atrocities, Norbert Burger, later formed the now-banned neo-Nazi NDP party with Schweiger. Schweiger's involvement earned him his first spell in custody in 1962, but he was acquitted.
Despite his age, Schweiger still travels widely in Austria and Germany to teach "the fundamentals of Nazism" to underground cells of hardcore neo-Nazis who, over the past three years, he says, have started to infiltrate political parties such as the FPÖ. Indeed, one of his protégés was elected last week as a senior official to the right-wing German National Democratic Party's (NPD).
This caused a furore and the German weekly Die Zeit said Andreas Thierry's election was "a win for Hitlerists in the fight over the NPD's future direction". DÖW referred to Thierry as "a neo-Nazi from Carinthia".
Thierry is well-known in Austria following publication of the photos showing Strache in his camouflage military uniform. Thierry was revealed to have been one of Strache's "paintball" partners.
Austrian journalist Wolfgang Purtscheller has spent his career documenting Austria's far right at great risk to his life. His summary of the situation in Austria is succinct.
"You have people like Schweiger - the puppet master in the mountains for half a century - able to form political parties while teaching people to make bombs, and the Burschenshaften with its history of terrorism and links to the mainstream parties. These are the intellectuals who hold the positions of power in society, in the police, the judiciary and in parliament. The neo-Nazis have learned by the mistakes of their past and are now working to build public support within the mainstream parties. Imagine what could happen if the FPO gets rid of the Verbotsgesetz," he said.
At the University of Vienna one of the Burschenschaften students brought Purtscheller's comments into sharp focus. "Muslims and immigrants are destroying our way of life. We are German-Austrians. We want a community here based on nationalism. We must fight to save our heritage and must fight for our culture. We are protesting that our freedom of speech is under threat," he said.
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