A woman found guilty of the manslaughter of a wedding guest in Londonderry is also seeking to have the verdict against her overturned.
Lawyers for all six today urged senior judges in Belfast to reopen their appeals based on a Supreme Court ruling on the interpretation of joint enterprise.
Those mounting renewed challenges include one of the men jailed for the fatal knife attack on north Belfast schoolboy Thomas Devlin.
Defence lawyers want the cases re-examined following a new finding on a law that allowed people to be convicted of murder even if they did not inflict the fatal blow.
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In February the Surpreme Court held that joint enterprise has been wrongly applied for more than 30 years.
The ruling, reached in the case of Ameen Jogee for the murder of former Leicestershire policeman Paul Fyfe in 2011, could eventually pave the way for hundreds of appeals.
Those now seeking to rely on that verdict are:
:: Nigel Brown, 32, one of two men convicted of killing Thomas Devlin on Belfast’s Somerton Road.
The 15-year-old victim was stabbed to death, and his friend seriously wounded, as they walked home from a shop in August 2005.
:: Barry Skinner, 36, jailed for his role in the murder of 22-year-old Alexander McKinley.
Mr McKinley was shot in the head as he sat in his sports car on Euston Street, east Belfast in October 2002.
:: Mark Kincaid, 34, one of three men found guilty of murdering hospital porter David Hamilton in 2004.
Mr Hamilton was bludgeoned to death with blunt objects at his flat in Belfast’s Ballybeen estate.
:: Peter Greer, 40, convicted of murdering Duncan Morrison and the attempted murder of Stephen Ritchie.
Gunmen shot the victims at a flat on Hazelbrook Avenue in Bangor, Co Down in May 2011.
:: Stephen McCaughey, 28, who was jailed for his part in the killing of farm labourer Philip Strickland.
Mr Strickland, 37, was shot in the face near Comber in January 2012.
:: Brenda Meehan, 47, found guilty of manslaughter in connection with the 2007 killing of Jim McFadden in Derry.
The 42-year-old was beaten to death at his home in the Shantallow area following a wedding reception in Co Donegal.
As the hearing got underway at the Court of Appeal, the five men involved in the challenge appeared together via a prison video-link.
Among those packed into the public gallery were Thomas Devlin’s parents, Penny Holloway and Jim Devlin.
Preliminary legal arguments centred on whether the court has jurisdiction to hear the cases, or if they should instead be sent to the Criminal Cases Review Commission (CCRC) - the body set up to examine potential miscarriages of justice.
Brendan Kelly QC, representing Brown, contended that the Jogee ruling established enough of a procedural flaw in all of the defendants’ original appeals to render those proceedings null and void.
On that basis, he submitted, Lord Justice Gillen, Lord Justice Weatherup and Mr Justice O’Hara should agree to examine claims of substantial injustice.
“This isn’t a change in the law, this is a case where the law has been corrected because all of us got it wrong,” Mr Kelly said.
He insisted that the court has “ample power” to reopen and hear the individual merits of the six appeals.
But Liam McCollum QC, for the prosecution, countered that the CCRC is the proper forum for assessing the cases.
He argued there was no irregularity in applying the law as it stood at the time of the original appeals.
“If you still have an opportunity to go to the CCRC you couldn’t say there would be an injustice by (the Court of Appeal) refusing to reopen the cases,” Mr McCollum added.
Judgment was reserved on the preliminary point on jurisdiction.