On Sunday, Ireland applied to the EU and the International Monetary Fund for a financial aid package to cover its fiscal needs and potential future capital requirements of its banking system.

EU finance ministers backed the request for aid, which an EU source put at 80-90 billion euros, to stop market concerns about Ireland's debt from spreading to other countries with big budget gaps such as Spain and Portugal, threatening a systemic crisis.

"In the short term this should be positive for risk appetite," said Peter Chatwell, rate strategist at Credit Agricole CIB in London. "It should be something Bunds see as a negative. I don't think this does anything to take Portugal and possibly Spain out of the firing line," he said.

German Finance Minister Wolfgang Schaeuble told ZDF television on Sunday his hopes were exactly the opposite.

"If we now find the right answer to the Irish problem, then the chances are great that there will be no contagion effects," he said.

But the effect may not last long.

"Will it prevent contagion? In the short-term, but not in the medium term. It only calms down markets and gives the other countries some room to breathe. Particularly, Portugal is not off the hook yet," said Carsten Brzeski, economist at ING.

The origins of the debt problems of Ireland and Portugal are different -- Ireland ran into problems because it had to help its banking sector, hit by the collapse of the real-estate market, while Portugal is suffering from low growth and lack of competitiveness.

But the end result was similar -- a debt burden that markets see as difficult to carry.

"I think it means Portugal is next (to request help)," said Filipe Garcia, economist at Informacao de Mercados Financeiros Consultants in the Portuguese city of Porto.

"I don't know if it will happen before the end of the year or after, but it's almost inevitable now," he said. "I think we've probably passed the tipping point of what is sustainable in terms of paying interest rates on debt."

If markets turn on Portugal, Spain may be next after that.

"If Portugal is forced to take a bailout then they'll turn their attention to Spain and I don't know what the government will do," said Edro Schwartz, economist at San Pablo University in Madrid.

The underlying problem for market mistrust of debt of some euro zone countries may only be solved with a quick and detailed solution for all euro zone countries, rather than a piecemeal approach, economists said.

The problem is that the euro zone started to go about it the wrong way.

Many economists and policymakers believe the current crisis is of German making because of Berlin's call to create a euro zone default mechanism under which private investors would take a hit, which scared investors and boosted spreads of Portuguese and Spanish bonds over Bunds to unsustainable levels.

"I still think that the main cause of contagion comes from the German proposal to include managed default in a future permanent crisis resolution mechanism," Brzeski said.

"As long as this issue is far from clear, speculation and possible contagion will stay alive," he said. "European politicians should now use the small window of opportunity they get from the Irish bailout to come up with a detailed and clear plan for the permanent crisis resolution mechanism."

EU leaders will discuss an outline of the mechanism to be prepared by the European Commission in mid-December.

(Reporting by Jan Strupczewski, editing by Jon Boyle)