Nat Fraser and Luke Mitchell are both serving life sentences
Two of Scotland's most high-profile killers are trying to persuade appeal judges to re-examine their cases.
Nat Fraser - convicted over wife Arlene's death - Luke Mitchell, who killed Jodi Jones sat side by side in court during their bids.
Fraser, 50, and Mitchell, 21, are serving life sentences but continue to protest their innocence.
They are now claiming at a legal debate before judges in Edinburgh that earlier appeals did not get a fair hearing.
Fraser was ordered to serve at least 25 years in 2003 for the "evil" and "cold-blooded" murder of 33-year-old Arlene, who vanished from Elgin, Moray, in April 1998.
The mother-of-two's body has never been found.
Judges threw out an appeal against his conviction. Fraser then asked judges at the Court of Criminal Appeal if he could appeal to the Privy Council. They refused that bid. Fraser's legal team claims that when the Court of Criminal Appeal in Edinburgh dealt with his challenge to his conviction it did not consider properly issues thrown up by human rights legislation.
Mitchell is serving a minimum of 20 years for the knife killing of his girlfriend Jodi Jones.
The 14-year-old's body was found in June 2003 in woods beside a path which joined her house in the Easthouses area of Dalkeith with the Mitchell home in the Newbattle district.
Mitchell claims he did not get a fair chance to present new DNA evidence because of difficulties getting legal aid to carry out scientific inquiries.
The latest challenges are seen as a last resort process used in Scottish criminal cases where there is no other form of redress.
A legal debate before Lord Justice General Lord Hamilton, sitting with Lords Kingarth, Eassie and Reed and Lady Dorrian continues on Friday.
Relatives of those involved in the cases have been watching proceedings.