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Voting took place in 19 countries on the fourth and final day of the election, in which the other eight EU member states have already finished voting.
Although centrist parties are expected to remain the dominant forces in the 736-member assembly, which shapes many EU laws and authorizes the EU budget, some far-right parties could make gains if the turnout is particularly low.
Parliament will start releasing results at 2000 GMT after the last ballot station closes. Exit polls from voting in the
"It doesn't look like the elections are a going to a be a triumph or a grand moment for European democracy," said Thomas Klau of the European Council on Foreign relations.
"National governments have set the perception that
Opinion polls before the election began suggested fewer than half the 375 million electorate would vote.
Many voters are worried by rising unemployment and say the EU has done too little, too late, to tackle the economic crisis, although it eventually agreed a fiscal stimulus plan which poured in money to try to revive the economy.
Others say the EU is too distant and has little impact on their daily lives. Some simply do not understand a system in which the parliament shares power with the executive European Commission and a Council of EU heads of state and government.
VOTING ON NATIONAL ISSUES
Many voters were expected to vote on domestic issues, which is bad news for several national governments.
Voters also are likely to punish
Other countries where governing parties could suffer setbacks include
Voting took place on Sunday in
For Italian Prime Minister Silvio Berlusconi, the risk is that a series of scandals, such as his relationship with an 18-year-old, will hurt his center-right party's standing.
In
DUTCH DISENCHANTED
Dutch voters sent a worrying signal to EU leaders by pushing anti-immigrant leader Geert Wilders' Freedom Party in to second place with four of the 25 seats, only one fewer than the main party in the center-right coalition government.
EU leaders are also worried by the stance of Britain's Conservatives, who lead opinion polls before a parliamentary election that is due next year but could be held earlier if Prime Minister Gordon Brown cannot hold on to power.
The Conservatives want a referendum in
The parliament's tasks will include tightening regulation of the financial system to help prevent another global economic crisis. It will also have the final say in the make-up of the next European Commission, an important regulatory body.
If the