Sir Fred was replaced by Stephen Hester, while Sir Philip took over from Sir Tom McKillop.
But the bank's board does not believe chief executive Stephen Hester needs to resign.
Mr Tyrie praised RBS chief executive Stephen Hester for taking full responsibility for the failure.
Stephen Hester, the chief executive, thinks so, reckoning that next year could see it turn the corner.
Chief executive Sir Fred Goodwin also announced his resignation at the meeting, and was replaced by Stephen Hester.
Stephen Hester was hired as chief executive by the previous Labour government to cut the bank's colossal debts.
The witnesses are the chairman and chief executive of Royal Bank of Scotland Group (RBS), Sir Philip Hampton and Stephen Hester.
The recovery programme is being "elongated", according to chief executive Stephen Hester.
Faced again with calls for a break-up of RBS, Stephen Hester has reformulated his argument that big and complicated banks haven't been the problem.
Recently, RBS's chief executive Stephen Hester insisted that the bank's return to the private sector was on track and could be completed within two years.
Next Monday, it's the turn of Stephen Hester and Sir Philip Hampton in front of a panel that, oddly, includes the new Archbishop of Canterbury.
The bank's chief executive, Stephen Hester, said in January that RBS was ahead of schedule with the most complicated restructuring ever undertaken by a company.
PLC, Stephen Hester, has already given up his bonus, for the second year running, after a computer problem left millions of customers without access to their accounts.
Last year, RBS's chief executive, Stephen Hester, waived his bonus.
Royal Bank of Scotland chief Stephen Hester had "no great problem" with greater transparency on pay and bonuses, Mr Miliband claimed, but Mr Cameron was failing to push ahead with the measures.
One of those could be the Royal Bank of Scotland, whose chief executive Stephen Hester has told the Guardian newspaper that he expects his bank to face penalties.
Sitting alongside him, Stephen Hester made clear that he'll go if he loses the confidence of his bosses, meaning both the board of directors and his majority shareholder, the Chancellor.
Stephen Hester wants to get that under way as soon as possible - at least a small element of it as a symbolic start to RBS returning to financial health.
Stephen Hester, chief executive of the Royal Bank of Scotland (RBS), says there is a risk to "turn over rocks and find new things" that are still problems in the banking industry.
Eric Daniels of LBG said his bank was contractually obliged to pay bonuses to employees of the former HBOS. Stephen Hester of RBS had similar obligations to employees of the former ABN AMRO.
"I'm glad that eventually Stephen Hester has seen sense and seen the outrage of most people in this country, and Lib Dems who have been complaining bitterly about this for weeks, " he said.
What Sir Philip and his chief executive, Stephen Hester, can't control is what happens to RBS's share price - which will have a big bearing on whether the Chancellor, George Osborne, wants to start the privatisation.
Stephen Hester, the RBS chief executive recruited on a commercial contract by the previous Labour government to salvage the stricken bank, found himself pilloried on tabloid front pages (photographs of him riding to hounds saw heavy use).
ECONOMIST: A bitter row about executive pay is about something bigger
That said, some would say he is unlucky that at two of the other British banks expected to be punished, Lloyds and RBS, the chief executives - Stephen Hester and Antonio Horta-Osorio - were elsewhere when the alleged wrongdoing took place.
Two other bank bosses have waived their bonuses this year follow scandals: Antony Jenkins following Barclays' admission of its involvement in rigging the multi-trillion-dollar Libor interest rate and Royal Bank of Scotland's Stephen Hester after a massive computer failure caused payments into customers' accounts to be delayed by several days.
Barclays ( BCS - news - people ) CEO John Varley and President Bob Diamond, RBS Chief Executive Stephen Hester is deferring his bonus this year in an attempt to show some humility in front of a British public still angry with the behavior of the banking system.
As for George Osborne's decision to require RBS to slim down its investment banking even further, and to retreat into being more of a UK bank, the word from the Royal Bank is that he's simply falling into line with chief executive Stephen Hester's blunt assessment with his third quarter results last month.
Speaking to Today presenter John Humphrys, Stephen Hester, chief executive of RBS, said that a "level playing field" is important for bankers' bonuses in the European Union and explained that his role is to "try to align RBS pay with things we want our people to do with customers and society as a whole".
But, interestingly, Stephen Hester has conceded - I think for the first time - that it will take longer than the promised five years for RBS to hit new targets for what he calls "value drivers", which are the profit that the bank earns relative to its equity capital, and its costs relative to income.
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