* Dealing with bust banks crucial step in banking union

* Euro zone ministers meet to discuss who pays for clean up

* Banks face moment of truth in ECB health checks

By John O'Donnell and Robin Emmott

LUXEMBOURG, Oct 13 (Reuters) - Euro zone countries will consider on Monday how to pay for the repair of their broken banks after health checks next year that are expected to uncover problems that have festered since the financial crisis.

Nobody knows the true scale of potential losses at Europe's banks, but the International Monetary Fund hinted at the enormity of the problem this month, saying that Spanish and Italian banks face 230 billion euros ($310 billion) of losses alone on credit to companies in the next two years.

Yet five years after the United States demanded its big banks take on new capital to reassure investors, Europe is still struggling to impose order on its financial system, having given emergency aid to five countries.

Finance ministers from the 17-nation currency area meeting in Luxembourg will tackle the issue of plugging holes expected to be revealed by the European Central Bank's health checks next year.

The president of the European Central Bank underscored the need for action in Washington at the meetings of the International Monetary Fund and the World Bank.

"The effectiveness of this exercise will depend on the availability of necessary arrangements for recapitalising banks ... including through the provision of a public backstop," Mario Draghi said on Friday. "These arrangements must be in place before we conclude our assessment," he said.

But the ministers' talks face an additional hindrance because Germany's finance minister, Wolfgang Schaeuble, is not expected to attend the two-day Luxembourg meeting. Germany, Europe's biggest economy, in in talks to form a new government.

During the region's debt turmoil, the European Union conducted two bank stress tests, considered flops for blunders such as giving a clean bill of health to Irish banks months before they pushed the country to the brink of bankruptcy.

The ECB's new checks are seen as the last chance to come clean for the euro zone as the bloc tries to set up a single banking framework, known as banking union.

The debate opens amid ebbing political enthusiasm for banking union - originally planned as a three-stage process involving ECB bank supervision, alongside an agency to shut failing banks and a system of deposit guarantees. It would be the boldest step in European integration since the crisis.

"We have to find a solution now," said Michel Barnier, the EU Commissioner in charge of financial regulation, urging faster progress in the slow talks. "The next financial crisis is not going to wait for us."