Lockerbie bomber appeal set to start in Scotland
Scotland's most senior judge, Lord Justice General Colin Sutherland, and four other judges at the country's highest criminal court will hear the case via video link.
The legal team for Megrahi's family will take part remotely from Glasgow. The case is due to last for three to four days with a ruling at a later date.
The family's lawyer, Aamer Anwar, said Megrahi's conviction has been described as "the worst miscarriage of justice in British legal history".
He added: "There can never be a time limit on justice. The families who support this appeal have never given up their search for the truth."
Megrahi was the only person convicted of bombing Pan Am Flight 103, which was blown up as it travelled from London to New York over the Scottish town of Lockerbie on December 21, 1988.
A total of 270 people from 21 countries were killed - 243 passengers, 16 crew, and 11 people on the ground - in what remains Britain's biggest terrorist attack.
Three Scottish judges sitting at a special court sitting in the Netherlands jailed the former Libyan intelligence officer for life in 2001, recommending he serve at least 27 years.
His first appeal was dismissed in 2002 but he was released in 2009 after being diagnosed with terminal cancer. He returned to Libya, where he died in Tripoli three years later.
His family's appeal was referred to the High Court of Justiciary in Edinburgh by the Scottish Criminal Cases Review Commission (SCCRC) in March.
The SCCRC ruled a possible miscarriage of justice may have occurred on the grounds of an "unreasonable verdict" in that it could not be proved Megrahi bought the suitcase that contained the bomb.
It also highlighted "non-disclosure" of evidence to Megrahi's defence team.
It has been widely claimed that the bombing was ordered by Iran and carried out by a Syrian-based Palestinian group, in retaliation for a US Navy strike on an Iranian Airbus six months earlier in which 290 people died.
Late last Friday, the High Court upheld a secrecy order signed by UK foreign secretary Dominic Raab to withhold intelligence documents related to the case.
Disclosure would cause "real harm" to UK international relations and national security with regard to counter-terrorism liaison and intelligence-gathering.
The documents are thought to allege a Jordanian intelligence agent within the Popular Front for the Liberation of Palestine-General Command (PFLP-GC) built the bomb.
The PFLP-GC has been designated a proscribed terrorist group by several countries, including Britain and the United States.
Lawyers acting for the Megrahi family believe the documents are central to their appeal.
In August, Raab signed a public interest immunity certificate to keep the documents secret.
In 2008, then-foreign secretary David Miliband also refused to release the papers before Megrahi's second appeal, which was started in 2007 but abandoned after Megrahi's diagnosis.
Agencies contributed to this report.