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8 year oldBoth are senior managers and have a long track record with Fox.
Mr Ailes resigned in July after a series of sexual harassment allegations against him by female news presenters. He has denied any wrongdoing.
Fox News plays a prominent role in US election coverage.
The channel's more conservative tone is popular among many Republican voters.
Mr Abernethy is chief executive of Fox Television Stations, running the 28 Fox-owned channels, and Mr Shine is senior executive vice-president and close aid to the company's founder Rupert Murdoch.
The men will divide the tasks of running the Fox News Channel and Fox Business Network. Mr Abernethy will focus on finance, advertising sales and distribution, while Mr Shine will manage the programming.
"While this has been a time of great transition, there has never been a greater opportunity for Fox News and Fox Business to better serve and expand their audiences. Together with our worldwide team of dedicated professionals, we are the most influential and powerful brand in television," said Mr Murdoch.
Mr Murdoch has taken over the role of Fox News CEO and executive chairman since Mr Ailes stepped down.
Mr Ailes had run the Fox News Channel since its beginning in 1996.
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