That question has put markets on edge amid the continent's government debt crisis, and European Union leaders hope to make a big step toward restoring confidence with the publication later this month of "stress tests" on 91 banks representing the bulk -- 65 percent -- of the banking system.
Still, skepticism persists about whether the tests will be tough enough to offer credible reassurance to financial markets worried that banks might be hiding losses on government bonds or other debt from troubled countries such as Greece, Portugal and Spain.
Doubts remain whether announcement of the results July 23 will be the magic bullet that stems months of anxiety -- or another missed opportunity by EU leaders, whose delays in agreeing on a $1 trillion backstop for troubled countries on the union's periphery worsened the crisis and helped bring Greece to the brink of bankruptcy.
The publication provides a "make-or-break challenge for the eurozone, a one-shot opportunity to clean up the banking system, bolstering balance sheets and investor confidence," said Marco Annunziata, an economist at UniCredit. He is "cautiously optimistic that Europe will not fail this test."
Such tests estimate what potential losses financial institutions could face if market conditions and the economy worsen over the next two years, and whether they would have enough funds to cope with resulting write-downs.
The key questions are whether the assumptions behind the tests are pessimistic enough to inspire confidence that the banks will stay afloat even if they hit more choppy water ahead -- or "reassurance through negativity," as Charles Stanley analysts put it.
Two questions remain unanswered: To what extent will the tests measure the bank's ability to withstand a collapse in the prices of government bonds? What will happen to banks that fail the test?
Europe has no single bank bailout fund like the U.S. Troubled Asset Relief Program, which was used to prop up the American banking system.
Stress tests conducted last year on the 19 biggest U.S. banks -- following the financial crisis that stemmed from losses on securities based on mortgages to people with shaky credit -- found that 10 needed to raise $75 billion total to withstand possible future losses.
Analysts questioned whether they were rigorous enough, but Federal Reserve Chairman Ben Bernanke said in May that making the results public bolstered confidence in the financial system.
European Central Bank President Jean-Claude Trichet voiced similar hopes for Europe's tests, saying Thursday that it is good for markets to see the results: "We think that it is confidence-building."
Karel Lannoo, the CEO of the Centre for European Policy Studies in Brussels, said "we just need to re-establish confidence by creating openness."
"What we've seen over the last weeks, months has been largely fueled by rumors that in fact our whole financial system has gone down the drain because of probably some limited problems here and there," Lannoo said.
France's finance minister, Christine Lagarde, has said the tests will show European banks are "solid and healthy."
EU leaders pledged June 17 to go public with the results -- a move that has helped power the euro from a dip to a four-year low below $1.19 to recent two-month highs around $1.27, and has helped stock markets rebound. It's a respite from the crisis that could vanish if investors think the test results are a fig leaf.
The list of banks being tested spans 20 countries, including non-eurozone Britain and Sweden. It includes big names such as Germany's Deutsche Bank AG and Commerzbank AG; France's BNP Paribas and Societe Generale; Spain's Banco Santander SA and Britain's Barclays and HSBC Holdings PLC.
It also features Spain's savings banks, or cajas , which were particularly exposed to the country's collapsed real estate sector, and Germany's public-sector Landesbanken, which already suffered hefty write-downs in the credit crisis.
German Finance Minister Wolfgang Schaeuble has said he believes that the tests' consequences for Germany "will be manageable."
The Committee of European Banking Supervisors, which is coordinating the exercise, says the tests will assume for their "adverse scenario" economic output 3 percentage points less than EU estimates over a two-year period.
They also will test a sovereign-risk shock in which market conditions are worse than those in early May, at the height of the eurozone debt crisis.
The tests will address "the risk of a strong fall in value of government bonds" but not a state bankruptcy, Lagarde told Germany's Handelsblatt business daily Friday.