The European Union said center-right parties were expected to take the most seats - 267 - in the 736-member parliament. Center-left parties were headed for 159 seats. The remainder were expected to go to smaller groupings.
Right-leaning governments were ahead of the opposition in Germany, France, Italy and Belgium, while conservative opposition parties were leading in Britain and Spain.
Greece was a notable exception, where the governing conservatives were headed for defeat in the wake of corruption scandals and economic woes.
Germans handed a lackluster victory to Chancellor Angela Merkel's conservatives and a historic defeat to their center-left rivals in the European Parliament vote months before a national election.
The Social D members, was expected to possibly win further seats as more results in Britain were announced.
Lawmakers with Britain's major political parties said the far right's advance was a reflection of anger over immigration issues and the recession that is causing unemployment to soar.
Near-final results showed Austria's main rightist party gaining strongly while the ruling Social Democrats lost substantial ground. But the big winner was the rightist Freedom Party, which more than doubled its strength over the 2004 elections to 13.1 percent of the vote. It campaigned on an anti-Islam platform.
In the Netherlands, Geert Wilders' anti-Islamic party took 17 percent of the country's votes, taking four of 25 seats.
The Hungarian far-right Jobbik party won three of 22 seats, with the main center-right opposition party, Fidesz, capturing 14 seats and the governing Socialists only four.
Jobbik describes itself as Euro-skeptic and anti-immigration and wants police to crack down on petty crimes committed by Gypsies. Critics say the party is racist and anti-Semitic.
Fringe groups could use the EU parliament as a platform for their extreme views but were not expected to affect the assembly's increasingly influential lawmaking on issues ranging from climate change to cell-phone roaming charges.
The EU parliament has evolved over five decades from a consultative legislature to one with the power to vote on or amend two-thirds of all EU laws. Lawmakers get five-year terms and residents vote for lawmakers from their own countries.
The parliament can also amend the EU budget - euro120 billion ($170 billion) this year - and approves candidates for the European Commission, the EU administration and the board of the European Central Bank.
Many Socialists ran campaigns that slammed center-right leaders for failing to rein in financial markets and spnti-treaty party Libertas, raised procedural questions about the opening of ballot boxes.
An exit poll in Poland showed Prime Minister Donald Tusk's pro-business Civic Platform party with 45.3 percent and the nationalist and conservative opposition Law and Justice party second with 29.5 percent - a shift to the center-right for Poland at the European parliament.
The Democratic Left Alliance-Labor Union garnered 12 percent. In Sweden, the Pirate Party, which advocates shortening the duration of copyright protection and allowing noncommercial file-sharing, looked set to take its first seat with 7.4 percent of the vote.
Britain, Ireland, the Netherlands and five other EU nations cast ballots over the last three days, while the rest of the 27-nation bloc voted Sunday.
---
Associated Press writers Geir Moulson and Patrick McGroarty in Berlin, Angela Charlton in Paris, Harold Heckle in Madrid, Raphael Satter and David Stringer in London, Constant Brand in Brussels, Pablo Gorondi in Budapest, Hungary, Ryan Lucas in Warsaw, George Jahn in Vienna, Derek Gatopoulos and Elena Becatoros in Athens, Barry Hatton in Lisbon, Alison Mutler in Bucarest, Romania, Keith Moore and Malin Rising in Stockholm and Veselin Toshkov in Sofia, Bulgaria, contributed to this report.
Get Action News on your website
