Strasbourg (France) (AFP) - The European Parliament elects a new president on Tuesday in a vote that promises to be stormy after a coalition aimed at keeping eurosceptics out of power broke down.

The winner will replace Germany's Martin Schulz, who during five years in office made the role far more powerful and prominent than it had ever been before.

The new president will lead the EU's only elected body, which will have the final say on a Brexit deal expected in two years time.

The 751 members of the parliament will cast secret ballots in Strasbourg, France. The vote can go to a maximum of four rounds.

The main candidates are both Italian: centre-right politician Antonio Tajani, and socialist Gianni Pittella. Another five candidates have little chance.

"I am almost sure the winner will have a link with Italy," joked Liberal candidate Guy Verhofstadt -- a former Belgian premier who owns a vineyard in Italy.

Schulz is meanwhile going back to politics in Germany.

But the contest has been a bitter one as a long-standing agreement between the two political groups broke down.

Tajani, a former spokesman for Italy’s Silvio Berlusconi and ex-European commissioner, is the candidate of the European People’s Party (EPP), the largest group in the assembly.

The EPP, which counts German Chancellor Angela Merkel as a member, says there was an agreement under a "grand coalition" that it should get the position, as a socialist, Schulz, held it last time.

The two groups have rotated the leadership of parliament between them for almost every year since the 1970s.

But Pittella says he will not accept an EPP "monopoly" of the EU’s top jobs, held by EPP members Jean-Claude Juncker, the European Commission president, and Donald Tusk, the head of the European Council.

A Tajani win could therefore prompt calls for a reshuffle of the top jobs, adding unwelcome instability to an already crisis-hit union.

Verhofstadt, the European Parliament’s Brexit negotiator, meanwhile saw his chances dip after a failed merger last week with Italy’s populist 5-Star Movement.

The grand coalition has been seen as limiting the influence of Eurosceptic groups led by Britain’s UKIP and France’s National Front, after they made stunning gains in the last European Parliament elections in May 2014.

The anti-EU movement has since gained strength, with Britons voting to leave the bloc in a shock referendum result last June, while across the Atlantic a similar wave of populism took Donald Trump to the US presidency.