Washington (CNN) After President-elect Donald Trump's surprise victory, far-right politicians in Europe crowed that it marked the beginning of a "destined" new world order that would soon see them rise to power too.

Destiny took a slight detour this weekend, however.

Austria's pro-European Green Party surprised observers and even the party's own supporters in defeating the Freedom Party, founded by former Nazis, in presidential elections Sunday. Instead, the so-called "Trump effect" struck in Italy, where anti-establishment voters rejected constitutional reforms, triggering Prime Minister Matteo Renzi's resignation.

The votes captured how polarized Europeans are by many of the same issues that propelled Trump to victory, including immigration, trade and economic malaise. Frustration over EU regulations also play a role as voters gravitate toward anti-establishment, anti-elite parties.

Austria might have demonstrated that the Trump Effect has limits, but both votes reflect complicated political currents and coming challenges that strike at the heart of Europe itself. Following Britain's unexpected June vote to leave the European Union, there's now the possibility of snap elections in Italy. And national elections are slated for France, Germany and the Netherlands in 2017.

"I don't think the wave of populism, the tide sweeping across the Atlantic, has been stopped by any means," said Alina Polyakova, a deputy director at the German Marshall Fund, referring to the Austrian results. "The idea of an Austrian Freedom Party candidate getting so close to leading the country was pretty much unfathomable a few years ago.

Trump himself has repeatedly criticized German Chancellor Angela Merkel over immigration, an issue that could hurt her at the polls, saying that because of her openness to taking Syrian refugees fleeing the war she "ruined Germany."

Marine Le Pen, the leader of France's National Front party who wants to end all immigration to France, told the BBC in November that Trump's win was an "additional stone in the building of a new world order destined to replace the old one."

The larger picture, says Mathew Burrows, director of the Strategic Foresight Initiative at the Atlantic Council, is of uncertainty for Europe itself as well as for its ties to the US.

"It's an inflection point," Burrows said. "I think this is really a breakup of the EU, not that the EU itself is going to go completely away, but it's the end of that vision that started at the end of the Second World War that Europe was going to unite."

Green Party surprise in Austria

The Austrian vote, on the surface, seems to be an embrace of Europe. The Green candidate, 72-year-old Alexander Van der Bellen, won with just over 53% of the vote without a robust campaigning structure, but with a clear pro-Europe stance.

Even so, a vote for Van see Bellen didn't represent a vote for the status quo. Voter anger meant that neither candidate representing the two mainstream parties made it into the second round of voting, according to the Eurasia Group. That meant that voters who didn't want a far-right candidate only had the choice of an independent with past ties to Austrian communists.

The Freedom Party hadn't explicitly argued for leaving the EU, but was harshly critical of the bloc and won the backing of those that want its dissolution, including Le Pen's National Front and Nigel Farage, former leader of the UK Independence Party.

In an echo of Trump's campaign, the Freedom Party candidate Norbert Hofer used the slogan "Austria First" and he echoed the anti-immigrant and anti-Islamic rhetoric that animated many of Trump's speeches as well as rightist and conservative parties across Europe.

Rosa Balfour, acting director of the Europe Program at the German Marshall Fund, said Austrians were reacting in part to the shock they saw in Britain after the so-called "Brexit" vote and in part as a counter-reaction to Trump.

"When Trump won, certainly it made populist leaders feel very empowered, but it's had a counter-effect," Balfour said from Brussels. "Citizens may feel frightened and aware that they can provoke extreme changes when all they wanted to do was protest against a particular government or figure."

After Hofer's loss, Iowa's Republican Rep. Steve King, who has referred to "sub-groups" to whites, tweeted a photo of the two of them and his condolences on the loss. "The cause of freedom & our friendship remain. Onward!" he wrote.

Yet Charles Lichtfield, an associate with the Eurasia Group, points to the fact that 46% of Austrian voters cast a vote for the Freedom Party.

"We should not assume that this eliminates the threat posed by a popular far right in Austria, or indeed elsewhere in the EU," he wrote in an analysis. Polling suggests that in the next election, the Freedom Party is likely to come first, he said, and form a coalition government.

Vote against Renzi

Polyakova and others said the Italian vote, widely read as another sign of the populist wave, is more complicated than that. In a move reminiscent of the way British Prime Minister David Cameron staked his position of the outcome of the Brexit referendum, Renzi said he'd step down if his push for constitutional reforms failed.

The coalition that assembled against him included anti-establishment groups such as the populist Euro-skeptic Five Star Movement. But it also included pro-Europeans, Balfour pointed out, and was about much more than anger about the Italian status quo.

The constitutional changes Renzi had suggested would give the executive branch of government more power than it had ever had and curtailed the Senate's legislative abilities, and were hotly debated publicly and on TV, she said.

JUST WATCHED Italians vote 'no,' a win for Eurosceptics Replay More Videos ... MUST WATCH Italians vote 'no,' a win for Eurosceptics 01:01

"Alongside the protest vote, the Euroskeptic vote, there was also a vote on the merits of the reforms, and then a generic vote against the prime minister, not necessarily out of populism, but simply" because some people didn't like Renzi and "he framed the whole referendum as a vote for or against him," Balfour said.