Both Rupert and James Murdoch face increasing pressure over allegations from former senior News International employees that they mislead parliament.
Tom Crone, formerly NI's top legal officer, and Colin Myler, editor of the News of the World until its closure, both raised questions over the veracity of James Murdoch's testimony to the culture media and sport select committee hearing on Tuesday.
Their contention is that James Murdoch was aware as early as 2008 that others were involved in phone-hacking.
The allegation is a serious one because a key facet of both James and Rupert Murdoch's evidence was that they were unaware of the extent of phone-hacking up until recently.
Labour MP Chris Bryant has called for the pair to be suspended from News Corporation by non-executives, while fellow leading parliamentarian on phone-hacking Tom Watson has referred the matter to the police.