For Poland’s Donald Tusk, the crushing defeat of Hungary’s illiberal prime minister, Viktor Orbán, after 16 years in office was evidence that the world was no longer “condemned to authoritarian and corrupt governments”.

Germany’s chancellor, Friedrich Merz, also believes the two-thirds majority secured by Orbán’s centre-right challenger, Péter Magyar, in Sunday’s elections was “a clear signal against rightwing populism” that showed “the pendulum is swinging back”.

But analysts warn that while the result of Hungary’s parliamentary ballot may have dealt Europe’s far right a temporary blow, it was far from marking a turn of the national-populist tide – and opponents would be foolish to see it as such.

“Of course there is a symbolic element,” said Sarah de Lange, an expert on the far right at the Netherlands’ Leiden University. “Europe’s longest-serving far-right leader, the inspiration for them all, was defeated – even when the system was rigged in his favour.”

But, de Lange said, Orbán’s defeat – after his fellow nationalists had rallied publicly around him in Budapest – was “not the defeat of his illiberal ideological model for how to organise a democracy when a far-right party is in power. That was not what motivated Hungary’s voters.”

Instead, the drivers were practical, and above all domestic: anger at corruption benefiting Orbán’s cronies; frustration with high prices, low wages and deteriorating public services including education and health; and a natural desire for change after four consecutive Orbán governments.

So the result “may dampen the far right’s mood for a bit,” said Gabriela Greilinger, a doctoral researcher specialising in Europe’s far right at the University of Georgia, particularly since Orbán “was such a central figure in bringing the global far right together” at events such as Cpac Hungary.

“But we really shouldn’t overestimate the impact,” Greilinger said. “The far right succeeds electorally because of domestic issues: this wasn’t the defeat of the far right, it was the defeat of Orbán’s kleptocratic, clientelistic, corrupt government.”

There may, analysts suggest, be some more concrete – but still limited – consequences if Magyar, as he has promised, can restrict the funding of the conservative thinktanks such as the Mathias Corvinus Collegium (MCC) and Danube Institute that Orbán endowed with hundreds of millions of euros in state and corporate funding.

“The MCC is the best-funded thinktank in Europe,” Greilinger said. “It actively seeks to influence European policy in Brussels, it has outposts in several other countries and it funds high-profile conservative researchers, including from the UK.”

The investigative outlet Democracy for Sale has detailed multiple links between Hungarian conservative thinktanks and prominent figures on the British right, such as the GB News presenter and unsuccessful Reform UK parliamentary candidate Matt Goodwin, who is listed as a “visiting fellow” of the MCC.

Beyond that, noted de Lange, the election result is also likely to lead to tensions within Europe’s far right over who, if anyone, should emerge as their next figurehead: a “mainstreamer” such as Italy’s Giorgia Meloni, or an EU-bashing “conflictualiser” in the Orbán mould.

But even if the result showed the far right, a “structural force” in most of Europe, can be defeated, it “does not offer a blueprint” for how to beat them anywhere else, or mark a “general turning point”, said Stijn van Kessel of London’s Queen Mary University.

Leonie de Jonge, an expert on the far right at the University of Tübingen in Germany, said the undoubted “short-term symbolic impact… doesn’t mean there’s going to be some kind of domino effect” on the rest of Europe’s far-right parties. “We absolutely have to get away from that idea.”

It is, in fact, “notoriously hard” to prove with actual data that far-right success or failure in one country has any electoral impact at all in another, noted Greilinger.

Europe’s nationalists themselves have offered various explanations for the defeat of their figurehead. Some, including Belgium’s defence minister, Theo Francken, and Alternative für Deutschland (AfD) figures, blamed Orbán’s close ties to Maga.

Donald Trump – who is deeply unpopular in Europe, including among many far-right voters – warmly endorsed Orbán, and Hungary’s outgoing prime minister invited the US vice-president, JD Vance, to stump for him, a move Francken called “stupid” and one AfD MP likened to “catching falling knives”.

But others in AfD, including the influential Maximilian Krah, have disagreed, arguing it was rather the corruption allegations swirling around Orbán, and his mismanagement of the economy, that cost him the election, while Italy’s Matteo Salvini has blamed Brussels for freezing EU funds.

Many, however, avoided drawing a firm conclusion, contenting themselves with saying that Orbán would be missed by “patriots” who backed “freedom, sovereignty and traditional values”. France’s Éric Zemmour insisted the loss was “neither ideological nor political” but circumstantial.

But if the key lesson of Sunday’s vote is that it is probably best to avoid failing to deliver what voters want (a fair cost of living, functioning services) while actively engaging in what they very much do not (state corruption), there may be some secondary lessons for Europe’s far right – and, by extension, their opponents.

The main one, de Lange argued, was that far-right parties were, clearly, vulnerable once they give their opposition a good reason to properly unite, perhaps in the face of an external crisis, or for a common cause – such as anti-corruption.

De Jonge saw a parallel with the eventual defeat of Brazil’s far-right leader, Jair Bolsonaro: “Strong, united democratic fronts, comprising voters from very different ideological backgrounds, coordinated across political parties, civil society and independent media, with a clear, hopeful message – they can defeat these regimes.”

It may be worth far-right parties thinking, too, about how far, once they are in power, they should try to rig the electoral system: Orbán’s gerrymandering was meant to boost his Fidesz party, but worked by boosting the largest party – so Magyar’s landslide was, at least partly, engineered by Orbán, Greilinger noted.

Some pundits argue that another clear lesson from Hungary’s vote is that Europe’s far right leaders should distance themselves from both Russia’s Vladimir Putin, whom Orbán cultivated, and Trump, whose administration’s stated objective is to promote anti-EU nationalists, but whose attempts to do so in elections have backfired.

Many populist leaders in Europe, to some extent, have already done so. But, said de Jonge, “I don’t think they’re all saying now that Orbán made some huge strategic error. They’re super-loyal to the broader ideological agenda they share, and they are not about to give that up. There may be some tactical adjustments. But it’s not a fundamental issue.”