The appeals court in Belfast has upheld a civil ruling in 2009 which held Michael McKevitt and Liam Campbell liable for the 1998 Omagh bombing.
However, a new hearing has ordered in respect of claims made against Colm Murphy and Seamus Daly.
In 2009, a judge found the men liable, awarding £1.6m damages.
Lawyers for the families had also appealed the compensation awarded. They said it should have been more because of the scale of the outrage. However, the relatives were told today the award would not be increased.
Michael Gallagher lost his son Aidan in the bombing. Outside court he gave this reaction to today's ruling............