They curried favor with President Trump and, following his lead, promoted conspiracy theories about the “deep state” and shadowy foreign forces working to oust them.

But when the time came, and the tide of voting went against them, the longtime leaders of Serbia and Hungary both stepped back from following the American president down the path of denying election defeat.

The quick acceptance of defeat in Serbia’s Oct. 25 general election by Aleksandar Vucic and, six months earlier, by Prime Minister Viktor Orban of Hungary, left Mr. Trump, who is still insisting that he won the 2020 presidential election, an outlier rather than a trendsetter in defying basic electoral arithmetic.

The concessions by even like-minded strongmen highlighted the gulf separating Mr. Trump’s denialism from the acceptance of reality. They also underlined yet again the question that looms over the most fiercely contested congressional races on Tuesday about whether the losers, from either party, will concede or challenge the balloting.

In Brazil’s recent presidential election, held on the same day as Serbia’s, Flávio Bolsonaro, the losing Trump-backed candidate, cried foul and demanded that the vote be annulled. But he fled to the United States instead of trying to mobilize his supporters to overturn the numbers, as his father, Jair, did after his own defeat in 2022 and Mr. Trump did two years earlier.

Other strongmen have taken a more Trumpian approach, like Nicolás Maduro, who was declared winner in a tainted election in 2024 and ruled Venezuela until United States forces plucked him from power this year.

So after years of running down democratic norms, the ready acceptance of defeat in Hungary and Serbia was not to be taken for granted. People close to the process said that the decisions were influenced, among other factors, by the fact that both leaders are angling for a return to power and that they lost so decisively that there was little room to manipulate the results.

Mr. Vucic, the master of a seemingly invincible political machine that dominated Serbia from 2012, carped on election night about “nonstop lying” by his foes and claimed that he had been “toppled” by foreign enemies, including “the American deep state — the one opposed to President Trump.”

Yet, to the surprise of both opponents and allies, Mr. Vucic prefaced his complaints with a simple statement: “It is clear that we have lost these elections.”

Christopher R. Hill, a veteran American diplomat who served as ambassador to Serbia under President Biden and assistant secretary of state under President George W. Bush, said of Mr. Vucic’s swift concession speech: “There is no way he would have ‘pulled a Trump.’ No way at all.”

“He knew he lost and lost big and wanted to get out ahead of the process,” Mr. Hill said, noting that his victorious opponents in a newly formed political bloc called “Student List-Students Win” have such divergent views that they could have trouble hanging together. This, he said, encouraged Mr. Vucic to believe “I’ll be back.”

Mr. Orban, too, believed that he would be back, using his concession speech after an April 12 election to try to rally his shellshocked Fidesz party for future battles. “We are not