Senior judges have set aside one week for the challenges by Colm Murphy and Seamus Daly.
Earlier this year the pair were held responsible for the Real IRA massacre following a civil retrial at the High Court in Belfast.
Murphy, a Dundalk-based contractor and publican, and his former employee Seamus Daly, from Cullaville, Co Monaghan, were sued by some victims' relatives in a landmark legal action.
A judge identified compelling and overwhelming evidence of their involvement in the August 1998 attack on the Co Tyrone market town.
Twenty nine people, including the mother of unborn twins, were killed in the blast.
Hundreds more were badly injured.