What exactly were they voting on?

The Nice Treaty, which was drawn up at the European Union's Nice summit in December 2000.

Among other things, the treaty changes the way decisions are taken within the EU, in the hope of preventing paralysis once it has taken on 10 new members.

Why were they voting on it?

The treaty had to be ratified by all the EU's 15 existing member-states. Ireland was the only country obliged by its constitution to hold a referendum.

The other 14 have already ratified it. Ireland held a referendum on the treaty in June 2001, but to the government's embarrassment voters rejected it.

Saturday's vote ensured that any future moves on the Nice Treaty will be put to a parliamentary vote in Ireland and not a popular referendum.

How important is the treaty?

The EU plans to conclude membership negotiations with 10 candidate countries by the end of this year, and to admit them in 2004.

Dublin avoided embarrassment as it would have looked very bad both at home and abroad if the Irish public had not given EU enlargement a vote of confidence.

Why did they reject it last time?

There were a number of reasons. Experts say the treaty might have been approved if more people had turned out to vote - nearly two out of every three voters stayed at home.

Most of them probably assumed that the Yes vote would win the day, as opinion polls had been predicting. The government, for its part, made very little effort to lobby for a Yes vote, while the No camp tried hard, and got its voters out.

The No campaign persuaded many Irish people that the treaty's support for joint EU action on defence would compromise Ireland's neutrality. In the event 54% of those who voted rejected the treaty.

What changed this time?

For one thing, the Irish Government ran a much more vigorous and high-profile campaign.

Its main message was that Ireland benefited greatly from EU membership, and it was now Ireland's turn to ensure that the 10 candidate countries from Eastern and Southern Europe got the same opportunities.

In general, the issue had been higher up the national political agenda, which in turn led to a higher turnout. The European Union also issued a declaration saying Irish neutrality would not be affected.

On the day, 63% of voters said Yes.

What other obstacles now stand in the way of EU enlargement?

Later this week in Brussels, EU heads of government will try to agree a framework for the financial aspects of enlargement.

But France, Spain and other members which benefit from the present system of subsidies, especially for farmers, are at odds with other members which want a firm plan to phase out many of those subsidies.

The collapse of the Dutch Government last week has also sparked speculation that the caretaker government may not endorse enlargement by the end of the year.

The present member-states are also demanding safeguard clauses to protect their own economies from the possible impact of enlargement.

What about the public mood?

In the Netherlands, public mood is hardening against the way the EU is evolving, and is leading demands for stricter standards to be applied in assessing whether the applicants are fulfilling many technical standards for entry to the EU club.

All this risks increasing the anti-EU sentiments which have grown more significant in several accession countries.

It could even lead to a shock rejection of membership by one or other of the applicants in referendums planned in some of them next year.

And that is not all. Assuming that EU leaders do approve the entry of the 10 new members at another summit in Copenhagen this December, that accession treaty must also be ratified by every member-state and by the European parliament.