"Rise" is a relative term, of course: only one German in eight actually voted for the AfD. But that is still shocking in a country that thought it had permanently excised all that old Nazi stuff from its politics.
And if you look more closely, the AfD's support was strongest in the same parts of the country that voted strongly for the Nazis in the 1933 election that brought Hitler to power.
The AfD was founded by an economics professor who just wanted Germany to leave the euro currency, but in the past four years it has been taken over by anti-Muslim, anti-immigrant ultra-nationalists, and they do sound a little bit like You-Know-Who at times.
Alice Weidel, the AfD's co-leader, has described Merkel's government as "pigs" who merely serve as "marionettes of the victorious powers of the Second World War, whose task it is to keep down the German people."
And the party's other co-leader, Alexander Gauland, said in an election speech last week: "We have the right to be proud of the achievements of the German soldiers in two world wars."
That sort of comment might be interesting to debate in a university seminar on German history, but 72 years after Hitler's death it is still too soon to say out loud in a Europe that was ravaged by German armies in World War II. Gauland, Weidel and their AfD colleagues are playing with fire and they are well aware of it.
The truly alarming thing, however, is not the occasional echo of the Nazis in AfD rhetoric. It is the fact that Germany is conforming to a general trend towards the authoritarian, ultra-nationalist right in Western politics.
Each country does it in its own historical style.
The pro-Brexit campaign in the United Kingdom last year was actually led by isolationist "Little Englanders". Their implausible promise of a glorious free-trading future for the UK outside the European Union was just a necessary nod in the direction of economic rationality - but the Brexiteers won because enough people wanted to believe them.
Similarly, Donald Trump fits comfortably into the American tradition: he is channelling American demagogues of the 1930 like Huey Long and Father Coughlin.
The economic situation of American workers and the lower middle class today is close enough to that of the 1930s that they responded to his mixture of nationalism, dog-whistle racism and anti-big-business thetoric by voting him into the presidency.
In France, Marine Le Pen appealed to nationalism, anti-immigrant sentiment and the resentment of the long-term unemployed to win almost 34 per cent of the vote in last May's presidential election. She lost, but the more important fact is that one-third of French voters backed the neo-fascist candidate. And now, in Germany, the AfD.
The common thread that runs through all these events, beyond the racism, nationalism and xenophobia, is economic distress.
The economies may be doing well, but a large proportion of the people are not. The gap between the rich and the rest was tolerated when everybody's income was rising, but that has not been true for 30 years now, and patience among the "losers" has run out.
This is still early days, but the direction of the drift in Western politics is clear, and it is deeply undesirable. The only thing that will stop it is decisive action to narrow the income gap again, but that is very hard to do in the face of the currently dominant economic doctrine.
Houston, we have a problem.
-Gwynne Dyer is an independent journalist whose articles are published in 45 countries.
