The U.S. Federal Reserve is keeping an eye on European banks struggling with the continent's debt crisis because of the turbulence in financial markets, one of the central bank's most influential policymakers said on Friday.

The reality is we monitor European banks and U.S. banks every day, so there's nothing to be particularly alarmed about that, William Dudley, the president of the Federal Reserve Bank of New York, told a gathering of New Jersey business leaders. That's a normal, standard operating procedure.

It's prudent for us to make sure that we understand what's going on, he said.

Dudley said the good news is that banks are in a stronger position than they were several years ago.

Capital levels are much higher, the quality of capital is much better, credit quality at the banks is improving, and the banks have huge liquidity buffers compared to what they had in 2008, he said.

There is some stress in the system right now ... But we're in much, much better shape than we were back several years ago, he said.

(Reporting by Edith Honan; Editing by Padraic Cassidy)