The prospect of a second presidential term for Donald J. Trump has many officials worried about alliance cohesion, NATO and the war in Ukraine.For most European governments, it is almost too upsetting to think about, let alone debate in public. But the prospect that Donald J. Trump could win the Republican nomination for the presidency and return to the White House is a prime topic of private discussion.“It’s slightly terrifying, it’s fair to say,” said Steven Everts, a European Union diplomat who is soon to become the director of the European Union Institute for Security Studies. “We were relieved by President Biden and his response to Ukraine,” Mr. Everts said, “but now we’re forced to confront the Trump question again.”Given the enormous role the United States plays in European security,” he added, “we now have to think again about what this means for our own politics, for European defense and for Ukraine itself.”The talk is intensifying as Mr. Trump, despite the Jan. 6, 2021, attack on the Capitol, his attempt to overturn the results of the 2020 election and his various indictments, is running well ahead of his rivals for the Republican presidential nomination and is neck-and-neck with President Biden in early opinion polls.In general, Central Europeans are more convinced that they can manage a second Trump presidency, but Western Europeans are dreading the prospect, especially in Germany, about which Mr. Trump seems to feel significant antipathy.During his presidency, Mr. Trump threatened to pull out of NATO and withheld aid to Ukraine as it struggled with a Russian-backed insurgency, the subject of his first impeachment. He ordered the withdrawal of thousands of American troops from Germany, a move later overturned by Mr. Biden, and spoke with admiration of President Vladimir V. Putin of Russia.Mr. Trump with President Vladimir V. Putin of Russia in Osaka, Japan, in 2019. Mr. Trump, who has praised the Russian leader, said he would end the war in Ukraine in a day.Erin Schaff/The New York TimesToday, with Europe and Russia locked in conflict over Ukraine, and Mr. Putin making veiled threats about nuclear weapons and a wider war, the question of American commitment takes on even greater importance. Mr. Trump recently said that he would end the war in a day, presumably by forcing Ukraine to make territorial concessions.A second Trump term “would be different from the first, and much worse,” said Thomas Kleine-Brockhoff, a former German government official who is now with the German Marshall Fund in Berlin. “Trump has experience now and knows what levers to pull, and he’s angry,” he said.Mr. Kleine-Brockhoff said he remembered talking with then-Chancellor Angela Merkel the night she returned from her first meeting with Mr. Trump as president. As usual, she was “all about managing the man as she had managed dozens of powerful men,” he said. “But no one will think” they can manage “Trump Two.”Several European officials declined to talk on the record about the prospect of another Trump presidency. They do not want to engage in American domestic politics, but they also may need to deal with Mr. Trump if he is elected, and some say they remember him as vindictive about criticism.Chancellor Angela Merkel of Germany engaging with Mr. Trump during a Group of 7 summit in Canada in 2018. Many of their exchanges were notoriously frosty.Jesco Denzel/German Federal Government, via Associated PressFor many European officials, Mr. Biden restored the continuity of the United States’ commitment to Europe since World War II: a dependable, even indispensable, ally whose presence eased frictions among former European rivals and allowed the continent to cohere, while providing an ironclad security guarantee.In the view of Mr. Trump and his supporters, that relationship allowed Europe to shirk spending on its own defense, a resentment that fueled Mr. Trump’s threats to reduce or withdraw American commitments.“The NATO alliance is not a treaty commitment so much as a trust commitment,” said Ivo Daalder, a former American ambassador to NATO. Given the doubts Mr. Trump raised in his first term, his return as president “could mean the end of the alliance, legally or not.”In conversations with Europeans, Mr. Daalder said, “they are deeply, deeply concerned about the 2024 election and how it will impact the alliance. No matter the topic, Ukraine or NATO cohesion, it’s the only question asked.”Jan Techau, a former German defense official now with Eurasia Group, said that in the worst case, a United States that turned its back would set off “an existential problem” for Europe at a moment when both China and Russia are working avidly to divide Europeans.President Biden delivering a speech in Lithuania during meetings with NATO leaders in July. In remarks, he affirmed his support for Ukraine in the war.Doug Mills/The New York TimesAbsent American engagement, “there would be a destructive scramble for influence,” he said.For Germany, Mr. Techau said, there would be the difficult question: Should Berlin be the backbone of a collective European defense without the Americans, or would it try to make its own deal with Russia and Mr. Putin?France would most likely try to step in, having long advocated European strategic autonomy, but few believe it can provide the same kind of nuclear and security guarantee for the continent, even together with Britain, that Washington does.President Emmanuel Macron of France has made it clear that he believes a politically polarized United States, more focused on China, will inevitably reduce its commitments to Europe. He has been pushing Europeans to do more for their own defense and interests, which are not perfectly aligned with Washington’s.So far he has largely failed in that ambition and, given the war in Ukraine, has instead embraced a stronger European pillar within NATO. But even Mr. Macron would not welcome an American withdrawal from the alliance.“It’s absolutely clear that Putin intends to continue the war, at least until the American elections, and hopes for Trump,” as does China’s leader, Xi Jinping, said Thomas Gomart, the director of the French Institute of International Relations. “It could be a big shock for Europeans.”A Trump victory, Mr. Gomart said, would most likely mean less American support for Ukraine, more pressure on Kyiv to settle, and more pressure on the Europeans to deal with Mr. Putin themselves, “which we are not ready to do militarily.”Ukrainian soldiers with an American tactical vehicle during training near Kyiv, Ukraine, in March. A Trump victory could mean less U.S. support for Ukraine.Mauricio Lima for The New York TimesThere is also concern that a Trump victory could breathe new life into anti-democratic forces in Europe.Mr. Trump’s victory in 2016 gave a major boost to European populist politics, and another victory would almost surely do the same, a major worry in France, where Marine Le Pen, a far-right leader, could succeed Mr. Macron.Even in Mr. Trump’s absence, the far-right Alternative for Germany, which Germany’s domestic intelligence agency has under surveillance as a threat to the Constitution, is for the moment the country’s second-most popular party.Dominique Moïsi, a French analyst with Institut Montaigne, a research organization, said a second Trump term would be “catastrophic” for Europe’s resistance to populism.Mr. Trump is a prince of chaos, Mr. Moïsi said, and with a war raging in Europe, and China open about its ambitions, “the prospect of an America yielding to its isolationist instinct” and embracing populism “is simply scary.”Not everyone in Europe would be unwelcoming, to be sure.Prime Minister Viktor Orban of Hungary has long celebrated ties to Mr. Trump and his wing of the Republican Party. Mr. Orban and his self-styled “illiberal democracy” is considered a sort of model by the hard right, especially his defense of what he considers traditional gender roles and of religion and his antipathy toward uncontrolled migration.Prime Minister Viktor Orban of Hungary speaking at a Conservative Political Action Conference gathering last year in Texas. He is revered by a wing of the American political right.Emil Lippe for The New York TimesIn Poland, too, the governing Law and Justice party shares many of the same views and criticisms of established elites. It had excellent relations with Mr. Trump and succeeded in getting American troops sent to Poland.“The view in the government and in a large part of the strategic community here was that the worst didn’t happen — he didn’t sell us out to the Russians,” said Michal Baranowski of the German Marshall Fund in Warsaw. “There was a feeling that the West Europeans were freaking out a bit too much,” he said.The big question for Poland, which has been fiercely pro-Ukrainian, is what Mr. Trump and the Republicans would do about Ukraine.Mr. Baranowski said that recent discussions in Washington with officials from the conservative Heritage Foundation had given him the impression that there would be significant continuity on Ukraine.“But Trump is unpredictable to an uncomfortable degree for everyone,” he said. More