Investment in the eurozone remains far below pre-crisis levels, partly due to problems in the banks, the Organisation for Economic Co-operation and Development (OECD) has said.
Bad debts at the banks are making them less willing to lend.
The OECD says many legacies of the area`s financial crisis are unresolved and major new problems have emerged.
Europe has, however, made "important progress" to recover from a double dip recession.
The eurozone`s economy has now been growing without interruption for three years. But it has not been strong growth, and it has been supported by what are called (perhaps euphemistically) the unconventional policies of the European Central Bank - extremely low, even negative interest rates and quantitative easing.
In its regular health check on the eurozone economy, the OECD notes that investment is far below 2007 levels, unlike the United States.
The reasons include weak demand - businesses will always be reluctant to invest if they are concerned that they may struggle to sell the goods and services they produce with the new investment.
But there are also some financial factors holding back investment. In some countries businesses are still burdened with high levels of debt.
The banks are struggling with high levels of "non-performing loans" - where borrowers are behind with their repayments. That tends to makes the banks more wary of new lending.
Two countries stand out as having particularly acute problems in this area - Greece and Italy, although they are not alone.
On one measure, the Italian banks look in even worse shape than their counterparts in Greece, the country whose economy has been most severely hit by the eurozone financial crisis.
The Italian banks have a higher level of non-performing loans compared to their capital, which is a financial buffer that is used to absorb losses, including losses due to problem borrowers.
Italy`s banks are seen as a serious weak link in the eurozone. The country`s economy has started growing again, but it remains 8.5% smaller than it was before the international financial crisis.
Italy`s government also has a problem with a persistently rising debt burden, behind only Greece in the eurozone. That in turn makes it a struggle for the government to bail out its banks, if they need it.
Indeed the OECD report warns about "the still large potential for negative feedback loops between banks and their sovereigns", although it doesn`t name Italy specifically in that context.
The eurozone`s banking union was intended to address that problem. The OECD says it needs to be completed. In particular the OECD says there should be more by way of eurozone-wide financial backstops - for a fund to deal with failing banks and for insurance to protect depositors if their bank goes bust.
These ideas are not popular in some eurozone countries, especially Germany where there seen as by many as a case of Germany underwriting the banks in other eurozone nations.
The wider message from the OECD report is that the eurozone may be out of immediate danger, but it is not in robust health.
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