In France, where Marine Le Pen's anti-EU National Front could emerge as the single largest group, official figures put the turnout at just over 35 per cent by mid-afternoon.
That compared with some 33 per cent at the same point in 2009, when the final French participation rate was a poor 40.6 per cent, below the European Union average of 43 per cent.
In Germany, which elects 96 MEPs, the most in the bloc, voter turnout by early afternoon was 25.6 per cent, up from 20.2 per cent and compared with its final turnout level of 43.3 per cent.
Despite generally pro-EU governments in eastern Europe where many former communist states joined the bloc in 2004, turnout rates have been low, some of them such as Slovakia on just 19.6 per cent.