There are some political moments that live in the memory. I vividly recall standing in the Place de l’Opéra in Paris watching Jean-Marie Le Pen address a rally during the 2002 French presidential election. Next to me were members of Forza Nuova, an Italian far-right party. It felt like a new and dangerous moment for European democracy.

Almost 20 years later, the far right are a more familiar part of the European political landscape. In France, Marine Le Pen, Jean-Marie’s daughter, now leads the Rassemblement National. The RN were disappointed this weekend when the party failed to win control of any French regions in elections. But the Le Pen party is considerably stronger than it was 20 years ago. Marine will carry the party banner into next year’s presidential election and has an outside chance of winning.

Most EU countries now have a significant far-right party. The term “far right” is, of course, contested. Some prefer labels such as rightwing populist. But the parties that sit together in the main far-right groupings in the European Parliament have fairly consistent traits. These include fierce hostility to immigration, particularly of Muslims; anti-elite rhetoric, shading into conspiracy theories; cultural conservatism, ultranationalism and dislike of the EU. Frequently there is also an equivocal attitude to the fascism of the 1930s — whether it is Vichy in France, Mussolini in Italy, Franco in Spain or the Nazis in Germany and Austria.

The shadow of the 1930s hangs over the European far right. It explained the outrage in the EU when Austria’s Freedom party first joined a coalition government in 2000, and the fear when Le Pen père got through to the final round of the French election in 2002. Back then, the choice seemed clear. Rightwing extremism would have to be crushed or democracy would be in peril.

Almost 20 years later, the situation is much more ambiguous. The far right is established across Europe. But it looks more like a chronic ailment than a mortal threat.

We have learnt that far-right parties can participate in governments without democracy ending as it did in 1933 after Hitler formed a ruling coalition in Berlin. Instead, parties characterised as far-right have joined governing coalitions in Austria, Italy, Estonia and Finland — and then lost power. Rather than ending, democracy adapts.

The far-right parties have, at times, compromised on some of their radical demands and lost popularity — which is what happened to the True Finns. Or they get caught up in tawdry scandals and lose popularity and power — as happened with the Freedom party in Austria and Ekre in Estonia.

But the process of democratic adaptation runs both ways. Many mainstream parties have adopted policies once championed by the far right in an effort to win over their voters. Denmark’s ruling coalition has taken an increasingly hard line on migration, threatening to return refugees to Syria on the dubious grounds that the country is now “safe”. In France, a prominent minister in President Emmanuel Macron’s government even accused Le Pen of “softness” on Islamism.

The next country where a party sometimes labelled “far right” may join a coalition is Sweden, whose government has just fallen. The Sweden Democrats, a party once deemed beyond the pale because of its roots in neo-Nazism, now seem close to a share of power. The Sweden Democrats have moderated their rhetoric and image. But any Swedish government they join would be likely to take positions on issues such as immigration and Islam that were unthinkable a decade ago.

Liberals will find this process depressing, even alarming. But, in many ways, it is how democracy is meant to work. Popular sentiment changes; political parties adapt.

However, it is still too soon to be completely sanguine about European democracy’s ability to absorb far-right politics. There are two big tests that may lie in the future. First, what happens when a far-right party governs, not in coalition, but on its own? Second, what happens if one of the EU’s major powers veers to the far right? This could happen in Italy, if the next government is based around two hard-right parties — the Brothers of Italy and the League. It could happen in France, if Le Pen wins the presidential election.

The evidence from Hungary and Poland is not encouraging about what the far right can do, unconstrained by coalition partners. Viktor Orban in Hungary has followed the classic strongman playbook of neutering the media and the courts to entrench himself in power. When Angela Merkel steps down as German chancellor later this year, Orban will become the EU’s longest-serving leader — which may reflect something more than his intrinsic appeal to voters.

The EU’s difficulty in accommodating a far-right leader is reflected in the increasing bitterness of the clashes between Orban and most other EU leaders. But Hungary is a small country, so its impact on the EU as a whole can be managed. If Le Pen won the French presidential election next year, the shock would be felt across the continent. It is conceivable the EU would break up under the impact. Alternatively, the EU might follow the pattern of Europe’s national democracies — and become an uneasy coalition between far-right and mainstream politicians.