Several older EU member states are opening up their labour markets to workers from the countries which joined the bloc on 1 May 2004.
EU enlargement exposed big gaps in living standards
Finland, Spain and Portugal said they would lift restrictions and Greece announced late on Friday that it would do the same.
They now join Britain, Ireland and Sweden, which opened their labour markets to new members two years ago.
But France, Germany and Austria are among countries keeping restrictions.
Austria and Germany say that geography makes their situation very different from states such as Britain or Portugal.
In Austria, many believe that more time is needed for poorer countries, such as neighbouring Slovakia, to build up their economies, the BBC's Jonny Dymond reports.
Only when the huge difference in the standard of living between Austria and Slovakia is reduced can Austrians see their labour market being opened.
Freedom of movement for workers is one of the key provisions of the EU treaties.
But some member states, especially Germany and Austria, were worried that their job markets would experience an influx of cheap labour from Eastern Europe, jeopardising job opportunities for their nationals.
EU LABOUR MARKET
1 May 2004: Britain, Ireland, Sweden allow in workers from eight new member states, but other 12 older EU states maintain restrictions
Workers from new members Cyprus and Malta do not face restrictions
1 May 2006: Finland, Greece, Spain and Portugal lift curbs on workers from the eight new member states in Central and Eastern Europe
2011: Deadline for all EU members to remove labour restrictions.
These fears prompted an EU-wide agreement that for a transitional period the existing member states could restrict workers from eight of the 10 states which joined in 2004.
Of the new member states, only nationals from Malta and Cyprus can travel freely to work in other member states.
It was agreed that for the other eight states - in Central and Eastern Europe - existing members could choose either to fully open up their labour markets or apply restrictions for up to two years after enlargement.
After that, restrictions can be extended for three more years then another two after that. But for the final two years countries need to provide evidence that their labour market would be seriously disturbed.
The eight former communist states which joined in 2004 have urged the older members to lift restrictions, arguing that these amount to discrimination. Hungary, Poland and Slovenia have even imposed reciprocal restrictions.
While Austria, Denmark and Germany are keeping full restrictions in place, three countries - Belgium, France and Luxembourg - look set to lift barriers gradually, sector-by-sector.
Italy is increasing its quota for foreign workers, while the Netherlands has postponed a decision on its labour market until the end of 2006.
Research published in Britain suggests that employers have gained major benefits from the influx of foreign workers since enlargement.
The research by the Joseph Rowntree Foundation found that highly-qualified workers from the new EU member states were filling many low-skilled and low-paid jobs, which British workers were not willing to accept.
The author of the report, Bridget Anderson, said many of the workers were prepared to accept the jobs in return for gaining experience and learning English, but she said that there were problems regarding the enforcement of the minimum wage, labour laws and conditions.
In February the European Commission published a report saying that the influx of mainly eastern European workers had stimulated the economies of Britain, Ireland and Sweden.