“On a world level, the situation that affects many countries is economic stagnation and the arrival of immigrants,” said Robert O. Paxton, a professor emeritus at Columbia University and one of the most prominent scholars of fascism. “That’s a one-two punch that democratic governments are having enormous trouble in meeting.”

Mr. Trump dismisses the labels used by those like Mr. Weld, a longtime Republican now mounting a quixotic campaign for vice president as a Libertarian. “I don’t talk about his alcoholism,” Mr. Trump said through a spokeswoman, “so why would he talk about my foolishly perceived fascism? There is nobody less of a fascist than Donald Trump.” (Mr. Weld, who in the 1990s reportedly appeared in public a few times having had too much to drink, declined to respond: “I’ll let that ride.”)…

Others caution against comparisons. “I read Kagan’s piece, of course,” said Volker Perthes, the director of the German Institute for International and Security Affairs, in Berlin. “All the phenomena he describes are raising concerns, but I would still not call Trump or his campaign fascist. Maybe with German and European history in mind, we are a bit more cautious than others in using the label ‘fascism.’”

Mr. Perthes said real fascism requires two more elements — an outright rejection of democracy and a harsher definition of order. Jobbik, the ultraright party in Hungary, would fall into this category, he said, but Norbert Hofer, the far-right candidate who narrowly lost the Austrian presidential vote, and Mr. Trump would not.