In 2001, Libyan-born Abdelbaset al-Megrahi was convicted of the 1988 bombing of Pan Am flight 103, Britain's worst ever act of terrorism.
The flight exploded 31,000ft above the Scottish town of Lockerbie, killing all 259 on board and 11 people on the ground.
He lost an appeal in 2002 but was granted a second hearing by the Scottish Criminal Cases Review Commission (SCCRC).
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He continued to protest his innocence until his death.
Who is appealing now?Megrahi's widow Aisha and son Ali are to submit files to the SCCRC, which will decide whether there are grounds to refer the case to the appeal court.
"The world will say sorry to my husband and my family one day," Aisha Megrahi said.
The BBC reports they will present concerns over the evidence which convicted Megrahi, including that given by Maltese shopkeeper Tony Gauci, who died last year.
Twenty-five UK-based relatives of the victims are set to back the appeal.
Do they have a case?According to the Daily Record, new grounds for appeal "include questions over the integrity of evidence produced by the Crown at the original trial, including circuit board fragments and clothes".
A relative of one of the victims remarked: "There are too many unanswered questions and the best place for the truth to come out is in a courtroom."
There are also questions about why then Scottish justice minister Kenny Macaskill, who sanctioned Megrahi's early release, met the prisoner shortly before he left prison, a move described as "extraordinary" by the family of one of the victims.
MacAskill said he would co-operate if called to give evidence.
