Three judges at the Court of Appeal in London will hear challenges by Kevin Liverpool and Junior Bradshaw.
The pair were found guilty of conspiracy to murder and conspiracy to rob following a three-week trial at Exeter Crown Court last year.
Liverpool was given a life sentence, with a minimum term of 10 years and eight months, while Bradshaw was jailed for 18 years.
The pairs were arrested near the star's home in Cullompton in June 2011.
Calls for MP to resign from city council
She has missed all her scheduled meetings since May
More of new Armada Way revamp revealed
"It will be marvellous when it is all done"
Exeter city councillor cleared after asylum hotel row
Alison Sheridan vindicated of any wrong-doing
M5 reopens following crash in Devon
Motorway between Cullompton and Exeter busy
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Over 1,000 took part in consultation
Parking fees rise at two Devon attractions
Increase of 10 percent
