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England will employ separate head coaches for the Test and limited-overs teams in a new era following Chris Silverwood's sacking.
Silverwood paid the price for a 4-0 Ashes thrashing in Australia when he was relieved of his duties early in February.
Joe Root then quit as Test captain before Rob Key was appointed as managing director of England men's cricket this month.
Key replaced Andrew Strauss, who took the role on an interim basis following the sacking of Ashley Giles in the wake of a nightmare tour Down Under.
Former England batter Key was expected to revert to different coaches for the red and white-ball sides and advertisements have now been posted for those roles.
The England and Wales Cricket Board (ECB) set a deadline of May 6 for applications, with the first interviews to take place on May 9 and 10.
Gary Kirsten, Simon Katich, Tom Moody are Graham Ford are among the names to be linked with the Test job.
England start their next Test against New Zealand on June 2 and begin an ODI series versus Netherlands on June 17.