WASHINGTON — The comparison was inflammatory, to say the least. Former Gov. William F. Weld of Massachusetts equated Donald J. Trump’s immigration plan with Kristallnacht, the night of horror in 1938 when rampaging Nazis smashed Jewish homes and businesses in Germany and killed scores of Jews.

But if it was a provocative analogy, it was not a lonely one. Mr. Trump’s campaign has engendered impassioned debate about the nature of his appeal and warnings from critics on the left and the right about the potential rise of fascism in the United States. More strident opponents have likened Mr. Trump to Adolf Hitler and Benito Mussolini.

To supporters, such comparisons are deeply unfair smear tactics used to tar conservatives and scare voters. For a bipartisan establishment whose foundation has been shaken by Mr. Trump’s ascendance, these backers say, it is easier to delegitimize his support than to acknowledge widespread popular anger at the failure of both parties to confront the nation’s challenges.

But the discussion comes as questions are surfacing around the globe about a revival of fascism, generally defined as a governmental system that asserts complete power and emphasizes aggressive nationalism and often racism. In places like Russia and Turkey, leaders likeVladimir V. Putin and Recep Tayyip Erdogan employ strongman tactics. In Austria, a nationalist candidate came within three-tenths of a percentage point of becoming the first far-right head of state elected in Europe since World War II.

In Hungary, an authoritarian government has clamped down on the news media and erected razor wire fences to keep out migrants. There are worries that Poland may follow suit. Traditional parties in France, Germany, Greece and elsewhere have been challenged by nationalist movements amid an economic crisis and waves of migrants. In Israel, fascism analogies by a former prime minister and a top general have again inflamed the long-running debate about the occupation ofPalestinian territories.

“The crash of 2008 showed how globalization creates losers as well as winners,” said Mark Leonard, the director of the European Council on Foreign Relations. “In many countries, middle-class wages are stagnant and politics has become a battle over a shrinking pie. Populists have replaced contests between left and right with a struggle between cosmopolitan elites and angry nativists.”

That dislocation may not lead to a repeat of Europe in the 1930s, but it has fueled a debate about global political trends. There is a tendency at times to try to fit current movements into understandable constructs — some refer to terrorist groups in the Middle East as Islamofascists — but scholars say there is a spectrum that includes right-wing nationalism, illiberal democracy and populist autocracy.

“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.”)

Americans are used to the idea that other countries may be vulnerable to such movements, but while figures like Father Charles Coughlin, the demagogic radio broadcaster, enjoyed wide followings in the 1930s, neither major party has ever nominated anyone quite like Mr. Trump.

Charles Grant, the director of the Center for European Reform, in London, distinguished between far-right nationalist parties like Marine Le Pen’s National Front in France and actual fascism.

“Historically, it means the demonization of minorities within a society to the extent that they feel insecure,” he said. “It means encouraging the use of violence against critics. It means a bellicose foreign policy that may lead to war, to excite a nationalist feeling. It takes xenophobia to extremes. And it is contemptuous of a rules-based liberal order.”

The debate about terminology may ignore the seriousness of the conditions that gave rise to Mr. Trump and his European counterparts. The New York real estate developer has tapped into a deep discontent in a country where many feel left behind while Wall Street banks get bailouts, newcomers take jobs, terrorists threaten innocents and China rises economically at America’s expense.

“It seems to me in developed and semideveloped countries there is emerging a new kind of politics for which maybe the best taxonomic category would be right-wing populist nationalism,” said Stanley Payne, a professor emeritus at the University of Wisconsin-Madison. “We are seeing a new kind of phenomenon which is different from what you had” in the 20th century.

Roger Eatwell, a professor at the University of Bath, in England, calls it “illiberal democracy,” a form of government that keeps the trappings of democracy without the reality.

“Elections are seen as important to legitimizing regimes,” he said, but instead of imposing one-party rule, as in the past, today’s authoritarians “use a variety of devices to control and/or manipulate the media, intimidate opponents” and so on.

The problem, she added, is that “the Western political leadership at the moment is too weak to fight the tide.”

Either way, it has found pockets of support on both sides of the Atlantic. Lilia Shevtsova, a political analyst in Moscow, said neo-fascism in liberal societies in the West stems from crisis or dysfunction while in illiberal countries like Russia and Turkey it reflects an attempt to fill the void left by the failure of Western notions to catch on.