WASHINGTON — Current and former executives of the big international bank HSBC are apologizing for lax controls but say they weren’t fully aware of illicit transactions flowing through the bank.

The executives are testifying at a hearing by the Senate Permanent Subcommittee on Investigations. Its investigation found that weakness at HSBC allowed Mexican drug cartels to launder billions of dollars through its U.S. operation and many other risky transactions.

The executive who headed HSBC’s Mexican affiliate in 2007 and 2008 says he tried to clean up deficiencies he found. David Bagley, the head of compliance for HSBC’s parent, said he lacked full authority over the bank’s far-flung affiliates, which each had their own compliance officer.

Senators are skeptical that the bank executives didn’t know about problems that persisted for seven years.