The world financial system is facing new peril as problems emerging on both sides of the Atlantic are causing economic turmoil just three years after a near-collapse in global markets.

In Europe, Greece is at risk of defaulting on its debts, which could have ripple effects from the French banks to the money-market funds where Americans park trillions of dollars in cash. In the United States, the showdown over raising the debt ceiling could disrupt repayment of U.S. Treasury debt, a key player in the functioning of global financial markets.

Among bankers, central bankers and private economists, there is a rising wariness, an ominous sense that the stabilization in world financial markets over the past two years could easily come unglued in the coming months. Money is now flooding into assets viewed as safe, such as German government bonds, instead of riskier investments, such as stocks.

The worriers are haunted by the ghost of Lehman Brothers. The September 2008 bankruptcy of the investment bank triggered a series of catastrophic events on global markets — leading banks to the brink of failure, triggering government bailouts and creating a deep economic hole that most of the world is still trying to climb out of.

The Lehman collapse exposed the extraordinary degree to which different corners of the financial world are connected, and showed how quickly and unpredictably crises can spread. It also put the world’s top economic policymakers on high alert, determined not to let the same thing happen again.

The great unknown is whether the world financial system has truly become more resilient in the past several years or whether risks such as a Greek default or the delay of Treasury bond payments would push it back into the abyss.

The world’s two most powerful central bankers have both warned of terrible consequences if the situations are not handled correctly.

U.S. Federal Reserve Chairman Ben S. Bernanke said Tuesday that even a short disruption of payment on Treasury debt “could cause severe disruptions in financial markets and the payments system, induce ratings downgrades of U.S. government debt, create fundamental doubts about the creditworthiness of the United States, and damage the special role of the dollar and Treasury securities in global markets in the longer term.”

Treasury securities are viewed worldwide as the safest of safe investments, and Bernanke is essentially warning that if securities show any risk, it would be catastrophic.

Jean-Claude Trichet, the president of the European Central Bank, has struck a hard line on how to deal with Greece’s financial difficulties, arguing that any decision to force owners of Greek debt to take losses could cause massive financial disruption. For weeks, Germany has been a holdout in forging a deal with the other euro nations on a Greek bailout, insisting that private investors forgo being paid until the nation’s economy improves.

“We would say it is an enormous mistake to embark in decisions that would trigger a credit event,” Trichet said last week.

On Friday, Germany dropped its demands that private investors share the losses, a concession aimed at allaying fears of a Greek default. German Chancellor Angela Merkel and French President Nicolas Sarkozy announced a new proposal asking investors to volunteer to wait until Greece has stabilized its economy before demanding debt payments.

A Greek default could cause that country’s banking system to collapse, could destabilize the German and French banks that hold billions of Greece’s debt and could push up borrowing costs for already imperiled Ireland, Portugal and Spain.

And those are just the predictable consequences. There is also a risk that the multi-trillion-dollar market for “credit default swaps,” which investors have used to bet against Greek debt, could spread losses even further. Such markets for complex securities known as derivatives were a key factor in how the 2008 financial crisis spread so quickly and globally.

And in another echo of the 2008 crisis, a Greek economic collapse could even affect U.S. money-market mutual funds, many of which — 44 percent, according to one account — hold significant amounts of European bank debt. In September 2008, one such fund, the Reserve Fund, “broke the buck” as its value dropped below $1 a share. Americans began pulling cash out of those funds, until the Treasury and Federal Reserve stepped in to prop them up.

But while the political brinksmanship among U.S. lawmakers over the budget plan and among the euro nations over how to deal with economic woes pose considerable risks, they may not be the deciding factors in a potential global financial meltdown.

While the debt-ceiling debate in the United States isn’t pretty to watch, if it forces agreement on a long-term plan to rein in budget deficits, it could foster a stabler global economy. Values of U.S. Treasury bonds have risen in recent weeks, as investors appear to believe there is little chance of default.

In Europe, there are even more open questions. The German and French governments would like Greece’s creditors to voluntarily take losses to share the bailout burden with taxpayers in other European nations. But it’s not clear that yet another bailout would fix the underlying problem for the Mediterranean nation’s fiscal stability: an onerous, unaffordable level of debt. Moreover, Greece’s financial problems have been well documented for more than a year, and presumably banks and other investors have had enough time to gird themselves for losses.

But then, that’s what they said about Lehman Brothers when it ran into trouble a few months after the failure of Bear Stearns in 2008. And three years later, the world still doesn’t quite know whether this insanely complex, immensely interconnected financial system is more resilient now than it was then.