ANTI-MIGRANT violence in Germany has become so severe over the past year that it is a miracle that no refugee has yet been killed. In one case, inebriated thugs threw a Molotov cocktail through a window into a room where an 11-year-old refugee would have been sleeping, had he not crept into bed with his mother in another room. Another xenophobe fired a gun into a refugee home and hit a Syrian man in the leg. Elsewhere, someone lobbed a hand grenade into a processing centre for asylum seekers. It did not go off.

There were 13,846 “right-extremist” crimes in Germany in 2015, according to preliminary estimates, about 30% more than in 2014. Of those, 921 were violent. This year the pace has accelerated, especially in the former East Germany. On February 18th about 100 people in Clausnitz, in the eastern state of Saxony, tried to block a bus carrying 20 refugees, including children. In another Saxon city a cheering crowd interfered with firefighters dousing flames in a building being converted into an asylum home. One police chief warns of a “pogrom atmosphere”.

Fears of a xenophobic backlash in otherwise-tolerant societies have been rising since the refugee crisis began, and not only in Germany. Right-wing populism is also growing in the Netherlands, as well as in Sweden, which like Germany entered the crisis with liberal asylum policies that are now being tightened. But Germany has taken by far the most refugees, with 1.1m arriving last year alone. And because of its history, Germany is extra-vigilant about extremism on the far right. The supreme court will soon consider an attempt by the 16 federal states to ban the NPD, a party that looks and smells like a neo-Nazi party. Germany also has a small subculture of violent, explicitly neo-Nazi networks.

When it comes to less extreme populism on the right, however, Germany is an exception in the European Union: it has no far-right party as firmly established as France’s National Front or Austria’s Freedom Party. Germany’s political mainstream long seemed to have been inoculated by the Nazi past. As recently as 2014, a biannual survey of right-wing attitudes in Germany found that xenophobia, chauvinism, anti-Semitism and authoritarian longings were declining. Rightist worldviews were held by just 2.4% of the population, down from almost 10% in 2002. Yet even at the time, Andreas Zick of the University of Bielefeld, a co-author of the study, said the middle was fragile: xenophobia could increase again in a crisis.

It probably started growing in 2014, even before refugee numbers surged, when the “Patriotic Europeans Against the Islamisation of the Occident” movement, or Pegida, began weekly marches through Dresden. After waning last spring, it has waxed again with the refugee crisis. Meanwhile the populist Alternative for Germany (AfD) party, founded in 2013 to oppose euro-crisis bail-outs, has veered to the xenophobic right.

Pegida and the AfD have similar supporters. Pegida marchers tend to be older middle-class men anxious about social decline and cultural alienation, says Hans Vorländer, co-author of a new book on the movement. Pegida and the AfD have not merged, he says, only because their leaders loathe each other. But the AfD has ridden the anti-refugee backlash to score more than 10% in national polls. It is likely to do well in three regional elections on March 13th and to enter the federal parliament in 2017. Mr Zick thinks it has a potential voter share of 20%. Germany seems at last to be like the rest of Europe in having an entrenched populist party on the right.

Worse, the data Mr Zick is collecting for his next study, due in May, suggest that the middle of society is becoming radicalised. This is most evident in the rise of verbal aggression. A leader of the AfD recently suggested that border guards should “make use of their firearms” to keep refugees out. Facebook and Twitter are abuzz with hate speech. This “radicalisation of rhetoric blurs the boundaries between physical and verbal violence,” says Mr Vorländer.

Heiko Maas, Germany’s justice minister, is worried. He has invited his counterparts in the 16 states to a summit on March 10th to think up strategies against extremism. But as refugees continue to arrive, Germany’s tolerance and moderation are being tested as never before in its post-war history. The firewall it has built between respectable conservatism and the extreme right may be breaking down.