STRASBOURG, France, Jan 21, 2025 (BSS/AFP) - How to deal with Donald Trump's disruptive return to the White House and the tempestuous forays of his billionaire ally Elon Musk into European affairs?

EU lawmakers will launch the search for answers on Tuesday, as the 27-nation bloc walks a fine line between guarding its interests and avoiding the ire of the mercurial US leader.

Their debate at the European Parliament in Strasbourg, a day after Trump was sworn in under the dome of the US Capitol, is set to highlight the difficult dilemmas facing the old continent.

Since the Republican's electoral win in November, European Union leaders have sought to project confidence, insisting the bloc had learned how to deal with Trump and was prepared for his comeback.

Campaign trail promises to "take other countries' jobs", slap tariffs on US allies and halt aid to Ukraine barely elicited a reaction as Brussels insisted it was ready, come what may.

But as Trump's menaces and outbursts, including a threat to annex Greenland, piled on after the vote, some lawmakers have grown impatient with the EU's wait-and-see attitude.

"We share a lot of things with the Americans, but at the same time we must not be naive," warned Marie-Pierre Vedrenne, from the centrist Renew group.

"We must not let our actions be dictated to us by Donald Trump or Elon Musk."

Lawmakers will debate whether the EU can find a unified voice to confront a cantankerous Washington.

But parliament itself is divided on the issue and -- unlike many national assemblies -- holds little real power, particularly on foreign policy.

- 'Smelling fear' -

A majority of parliamentarians are likely to denounce the "interference" of the world's richest man in European politics -- after Musk publicly backed a far-right party in Germany's upcoming elections.

They will also up the pressure on the European Commission -- the EU's executive body -- to crack down on social media, including Musk's X, if found in breach of EU digital rules.

"When beasts smell fear they attack (with) double" the ferocity, said socialist lawmaker Laura Ballarin Cereza, voicing concern about the bloc's muted response to incursions by Musk and Trump into its affairs.

But the power duo have plenty of supporters too in Strasbourg, where they elicit fascination and adulation from some on the right.

A dozen lawmakers travelled to a freezing cold Washington to participate in the festivities linked to Trump's inauguration, as did Italy's hard-right Prime Minister Giorgia Meloni.

Far-right lawmakers, whose influence has grown following June European elections, have rejected calls for the commission to firmly apply the Digital Services Act -- the EU's landmark rules tackling illegal and harmful activities online -- which could place Musk at risk of copious fines.

"We are used to seeing this type of censorship under China or Cuba," said Alonso de Mendoza Asensi, a spokesman for the Patriots for Europe group.

"It's really troubling to witness this happening now in Europe".