It's being called a four-day "democratic marathon" in which 350 million people are eligible to choose a 25-country parliament.
The United Kingdom and the Netherlands began voting yesterday. Ireland and the Czech Republic are voting today. Polls open tomorrow in Latvia and Malta and on 13 June in all other EU states.
Partial results from the Netherlands show a drop in support for the governing Christian Democrats, although they still received slightly more votes than the opposition Social Democrats. Both parties now have the same number of seats -- seven.
The voting for the 732 deputies of the European Parliament comes little more than a month after 10 new member states -- mostly from Eastern Europe -- joined the EU. But those looking for enthusiastic voters on the streets of Prague, Warsaw, or Tallinn this weekend will probably be disappointed.
As the influential Swiss newspaper "Neue Zuericher Zeitung" said yesterday: "Journalists who ask questions of people in the street have to be prepared for bewildered looks: the so-called average citizen knows little or nothing about the European Parliament, or about the way its powers have grown in the last few years, or that now in some ways it is more important than national parliaments."
Polish political analyst Edmund Wnuk-Lipinski of the Institute of Political Studies in Warsaw says all the indications are that voter participation in the new EU member states will be low.
"Probably there will be a very, very low turnout in the European elections in post-communist countries. That is according to all opinion polls, which show a low participation in Poland and a number of other post-communist countries joining the European Union," Wnuk-Lipinski says.
Why such apathy, so soon after the 10 new members achieved in almost all cases good turnouts in national referendums to approve joining the EU? It's true that in the "old" EU states, voter apathy in European Parliamentary elections is almost traditional, much to the chagrin of the parliamentarians.
Analysts say the reasons for the lack of interest are basically the same in the East as in the West.
One reason, as already mentioned, is that most people in the new member states have very little knowledge of what the European Parliament actually does.
The second is that established national political parties have not given any attention to the election. As Brussels-based analyst Marco Incerti of the Center for European Policy Studies says, "The problem is, people don't see why their vote matters. And at the moment, all [that] the political parties are doing is mostly presenting celebrity candidates that can attract attention, like the famous top model in Estonia, or athletes in various other countries, astronauts and so on."
Incerti says that, in the short-term, this may bring people to the ballot box, but it is not necessarily a constructive policy, in that it is unclear how well these "celebrities" -- who often have no political experience -- will perform as serious deputies once they are in parliament.
Petr Drulak of the Czech Institute of International Relations acknowledges that there is a measure of "frivolity" in the European election that is absent from other polls. But he says that, for Czechs, it's a learning process.
"I don't see this as a major tragedy because both the country and the society have to get used to the European system. The important thing will be whether the deputies who are elected will be able to do any sensible work, and present this work to the voters. And then the next [European] elections will be important, because the deputies will be able to demonstrate what they did during their term," Drulak says.
There is another possible reason the European elections might be viewed with skepticism by the public.
An article this week in "The Times" of London puts it succinctly: "Many in the region believe that the candidates' main aim is not political, but personal: to enrich themselves through the generous expenses that each Euro MP receives. Under communism the state was seen as a milch cow, and it was almost a patriotic duty to appropriate as much as possible for personal benefit. Now Moscow's rule has been replaced by that of Brussels, and the new MEPs are keen to seize every opportunity for enrichment."
The deputies do, indeed, receive generous allowances -- for instance, some 3,700 euros ($4,445) a month for general expenses, including travel within their constituencies, and for office staff, plus a daily living allowance of 262 euros when they are in Brussels or Strasbourg. Plus, a separate travel allowance to and from those cities to their home countries.
In addition, they receive salaries based on the pay rates of national parliamentarians at home. In the case of Italian members of the European Parliament (MEPs), this means the salary is a hefty 11,000 euros per month. For the incoming Eastern Europeans, however, it may be as low as 1,000 euros a month.
Over the years, there have been allegations of abuse by deputies, such as overcharging on travel expenses and employing relatives at parliament's expense. Aware of this tarnished reputation, the last parliament under President Patrick Cox developed a package of reforms that would have given each deputy a standardized salary of 8,500 euros. It would also have reined in excessive expense claims.
But the package was rejected at the last minute by the EU's ruling Council of Ministers, with Germany saying the standard salary was too high.
This has left the new parliament to tackle this key issue of credibility. In the absence of any concrete reforms, several hundred candidates have reportedly signed pledges to adhere to a code of conduct eliminating abuse of expenses.