The agreement was hailed as a step forward for Greece, but doubts immediately emerged as to whether it would do much more than deal with its most pressing debt problems.

Greece will need more help if it is to bring its debts down to the level envisaged in the bailout and will remain "accident prone" in coming years, according to a deeply pessimistic report by international experts obtained by Reuters.

After 13 hours of talks, ministers finalized measures to cut Greece's debt to 120.5 percent of gross domestic product by 2020, a fraction above the target, to secure its second rescue in less than two years and meet a bond repayment in March.

By agreeing that the European Central Bank would distribute its profits from bond buying and private bondholders would take more losses, the ministers reduced Greece's debt to a point that should secure funding from the International Monetary Fund and help shore up the 17-country currency bloc.

The austerity measures wrought from Greece are widely disliked among the population and may present difficulties for a country which is due to hold an election in April.

Further street unrest could test politicians' commitment to cuts in wages, pensions and jobs. Greece's two biggest labor unions called a protest in Athens on Wednesday.

An opinion poll taken just before the Brussels deal showed that support for the two Greek parties backing the rescue package had fallen to an all-time low while leftist, anti-bailout parties showed gains.

Anastasis Chrisopoulos, a 31-year-old Athens taxi driver, saw no reason to cheer the deal.

"So what?" he asked. "Things will only get worse. We have reached a point where we're trying to figure out how to survive just the next day, let alone the next 10 days, the next month, the next year."

Parliaments in three countries that have been most critical of Greece's second bailout - Germany, the Netherlands and Finland - must now approve the package. German Finance Minister Wolfgang Schaeuble, who caused an outcry by suggesting that Greece was a "bottomless pit," said he was confident it would be passed.

"We have reached a far-reaching agreement on Greece's new program and private sector involvement that would lead to a significant debt reduction for Greece ... to secure Greece's future in the euro area," Jean-Claude Juncker, who chairs the Eurogroup of finance ministers, told a news conference.

The euro gained in Asia after the bailout was agreed.

Some economists say there are still questions over whether Greece can pay off even a reduced debt burden, suggesting the deal may only delay a deeper default by a few months.

Swedish Finance Minister Anders Borg said: "What's been done is a meaningful step forward. Of course, the Greeks remain stuck in their tragedy; this is a new act in a long drama.

"I don't think we should consider that they are cleared of any problems, but I do think we've reduced the Greek problem to just a Greek problem. It is no longer a threat to the recovery in all of Europe, and it is another step forward."

A return to economic growth in Greece could take as much as a decade, a prospect that brought thousands onto the streets of Athens to protest on Sunday. The cuts will deepen a recession already in its fifth year, hurting government revenues.

"We sowed the wind, now we reap the whirlwind," said Vassilis Korkidis, head of the Greek Commerce Confederation. "The new bailout is selling us time and hope at a very high price, while it doggedly continues to impose harsh austerity measures that keep us in a long and deep recession."

EXTRA RELIEF

A report prepared by experts from the European Union, European Central Bank and International Monetary Fund said Greece would need extra relief to cut its debts near to the official debt target given the worsening state of its economy.

If Athens did not follow through on economic reforms and savings to make its economy more competitive, its debt could hit 160 percent by 2020, said the report.

"Given the risks, the Greek program may thus remain accident-prone, with questions about sustainability hanging over it," the nine-page confidential report said.

The deal envisages a beefed up monitoring of Greece's implementation of the reforms - a move that could bolster accusations among some Greeks of interference in domestic affairs but which some critics say is essential.

Dutch Finance Minister Jan Kees de Jager, one of the most strident critics of Greece, told Dutch news agency ANP that he had bargained hard for the permanent monitoring mission.

"This program is not something to cheer about," he said.

BOND SWAP

The accord will enable Athens to launch a bond swap with private investors to help put it on a more stable financial footing and keep it inside the euro zone.

About 100 billion euros of debt will be written off as banks and insurers swap bonds they hold for longer-dated securities that pay a lower coupon.

Private sector holders of Greek debt will take losses of 53.5 percent on the nominal value of their bonds. They had agreed to a 50 percent nominal writedown, which equated to around a 70 percent loss on the net present value of the debt.

Juncker said he expected a high participation rate in the deal, but some bondholders may balk at the new terms.

Greece said it would pass legislation that would allow it to enforce losses on bondholders who will not take part.

Euro zone central banks will also play their part in reducing the debt.

A Eurogroup statement said the ECB would pass up profits it made from buying Greek bonds over the past two years to national central banks for their governments to pass on to Athens "to further improve the sustainability of Greece's public debt."

The ECB has spent about 38 billion euros on Greek government debt that is now worth about 50 billion euros.

The private creditor bond exchange is expected to launch on March 8 and complete three days later, Athens said on Saturday. That means a 14.5-billion-euro bond repayment due on March 20 would be restructured, allowing Greece to avoid default.

The vast majority of the funds in the 130-billion-euro program will be used to finance the bond swap and ensure Greece's banking system remains stable; some 30 billion euros will go to "sweeteners" to get the private sector to sign up to the swap, 23 billion will go to recapitalize Greek banks.

A further 35 billion or so will allow Greece to finance the buying back of the bonds. Next to nothing will go directly to help the Greek economy.

($1 = 0.7538 euros)

(Additional reporting by Luke Baker, Julien Toyer, Robin Emmott in Brussels, Daniel Flynn in Paris, Terri Kinnunen in Helsinki, Sarah Marsh in Berlin, Harry Papachristou in Athens; Writing by Mike Peacock and Elizabeth Piper; Editing by Giles Elgood)

• A Permanent Economic Emergency