By Marc Jones FRANKFURT (Reuters) - Two undisclosed banks tapped the European Central Bank for dollar funding on Wednesday, the second time in a month the facility has been used and the latest indication of the pressure the debt crisis has put on the euro zone banking system. A total of $575 million was borrowed by the two banks. The dollars, which are available as part of a swap deal the ECB has with the Federal Reserve, were offered at 1.1 percent, well above the price available to banks with access to open markets. While the ECB's weekly limit-free dollar and euro refinancing operations should ensure no euro zone bank falls victim to a funding drought, moves by U.S. money market funds and other traditional dollar providers to cut lending to Europe have added to current market jitters. Fears about the health of euro zone banks heavily exposed to the region's debt crisis has triggered a new wave of unease on financial markets and seen European bank shares lose a third of their value since the start of July. For graphic on European banking stress, click http://link.reuters.com/qux33s On Aug. 17, a single bank borrowed $500 million, the first time the facility was utilised since February. The latest use comes just hours after two of France's biggest banks, Societe Generale and Credit Agricole, were downgraded by rating firm Moody's over fears they may have to swallow writedowns on their Greek debt. Insuring bank debt is also more expensive than ever. The Markit iTraxx senior financials index, which expresses the cost of insuring the debt of 25 European banks and insurers, has plunged. Credit Default Swaps (CDS) on many top European banks are all also currently higher than after the Lehman Brothers collapse in late 2008. "The fact a couple of banks are obviously struggling to get dollars is just a sign of the times and a reflection of the current worries," said one trader who requested anonymity. "It hasn't really had any impact on the market," he added. (Reporting by Marc Jones; Editing by Toby Chopra)

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