People in 21 European Union member states are voting on the last day of the European Parliament elections.
The majority of almost 388m eligible voters, including German, French and Spanish citizens, are casting their ballots on Sunday at polling stations across the European Union.
Results are expected to be announced on Sunday evening.
One of the first tasks of the incoming parliament will be to elect a new president of the European Commission, the EU's executive body.
After years of economic crisis, rising unemployment and poor growth, many Europeans have come to question the wisdom of ever-closer EU integration and are expected to vote for Eurosceptic parties on the right or left that are promising radical changes.
According to the Reuters news agency, opinion polls suggest at least a quarter of seats in the parliament will go to anti-EU or protest groups, but around 70 percent will remain with the four mainstream, pro-EU blocs: the centre-left, centre-right, liberals and Greens.
Polls are also predicting that the centre-right European People's Party will secure around 220 seats, putting it 15 to 20 seats before the center-left Socialists and Democrats.
Turnout is expected to fall, dropping to about 40 percent from 43 percent in 2009.
While expectations ahead of the vote were that far-right groups would record historic victories in countries such as France, the Netherlands and the UK, exit polls from the Netherlands, which voted on Thursday, were a surprise.
Geert Wilders' anti-EU and anti-Islam Freedom Party came fourth rather than first, according to exit polls from Ipsos, the Paris-based research think-tank, with the majority voting for pro-EU parties.
Parliament leaders will meet on the morning of May 27 to discuss the results and the European Commission presidency; EU leaders meet in the evening on the same day.
However, it is expected to take several weeks before leaders decide on a name to put to a parliamentary vote.