London: This is not the first time that president-elect Trump has criticised either the EU or NATO. The latter especially was on high rotation in his campaign.
But when German foreign minister Frank-Walter Steinmeier arrived in Brussels on Monday to meet NATO secretary General Jens Stoltenberg, both were worried.
Mr Trump's comments in an interview with The Times of London had "caused astonishment and commotion", Mr Steinmeier said, adding pointedly "not only in Brussels".
The pair discussed it over breakfast. Germany's Foreign Office diplomatically tweeted that they were conferring over "current challenges".
The EU's foreign policy chief Federica Mogherini, an ambitious, consensus type (and pal of Australian Foreign Minister Julie Bishop), took a more optimistic line, after it became clear she couldn't dodge the issue altogether in her morning press conference.
She hoped to build a "partnership" between the EU and the Trump administration, she said – and claimed to have been given friendly signals by VP-elect Mike Pence.
But, she said pointedly, "so many things are not yet clear, even to the incoming administration".
And this is the source of their concern.
Only days now remain before the world starts to discover what actions lie behind president-elect Trump's words.
Europe's leaders know his rhetoric, from his bombastic stump speeches and abrupt tweets.
They have also received some soothing words in private, some assurances that his team will keep him in line. They have watched as he appointed mostly establishment insiders, rather than wreckers, to key positions.
But President Trump is a wild card, and that makes them nervous.
Criticism of the EU they can live with. All but the most starry-eyed have given up on TTIP, the trans-Atlantic trade deal-in-waiting. And while Mr Trump met with chief Brexiteer Nigel Farage, Marine Le Pen was left waiting in Trump Tower Foyer without a chance to ride the big gold lift.
Even if President Trump tried to meddle in Europe's labyrinthine domestic politics, it's unclear what effect he would have either on purpose or accidentally.
But his comments on NATO are more significant.
He has focused his complaints on the other members not pulling their weight financially - already a divisive issue that worries at the treaty's foundations.
And describing it as 'obsolete' implies that the pact is under existential threat. Possibly from him.
Many states, especially in Europe's north and east, consider a US-backed NATO to be one of the main elements keeping a lid on Russian efforts to rebuild a 'sphere of influence' in the region.
Some even believe that NATO's Article 5, the pact of mutual defence, to be the only thing keeping Russian tanks (mostly) inside Russia's borders.
In Brussels, and many other European capitals, a lot of breaths will be held over the coming weeks and months, as we wait to find what actions will follow Trump's words.
