Lawyers for Colm Murphy and Seamus Daly claimed the lawsuit against them should be thrown out due to a lack of evidence.
Both men are defending an action over allegations that they played central roles in the Real IRA attack in August 1998.
Relatives of some of the 29 people killed in the atrocity brought proceedings against them in an attempt to have them held liable.
Murphy, a Dundalk-based contractor and publican, and former employee Seamus Daly, from Culaville, Co Monaghan, were ordered to face a civil retrial after their appeals against being found responsible for the bombing were upheld.
Two other men held liable in the initial landmark ruling in 2009, convicted Real IRA leader Michael McKevitt and fellow dissident republican Liam Campbell, failed to have the findings against them overturned
During the new hearing in front of Mr Justice Gillen lawyers for the victims' families contended that Murphy supplied mobile phones to the bomb team.
Although he is not suspected of being in Omagh on the day of the bombing, a phone registered to him can be traced to within 5km of the town an hour before the blast, according to the plaintiffs' case.
Analysis of mast coverage led to the location being made.
Daly is allegedly linked by a call he allegedly made on one of the phones just after the explosion.
They have been challenged by senior counsel for the families to come to court and testify over the alleged telephone links.
Both men deny the claims against them, but there has been no indication yet that either will give evidence.
On Tuesday their barristers sought a direction that they have no case to answer.
Dermot Fee QC, for Murphy, argued that the plaintiffs have failed to produce sufficient evidence against his client.
It was accepted that a phone registered to the builder travelled from the Republic to the vicinity of Omagh on the day of the bombing.
But Mr Fee contended that this proved nothing.
Murphy was not in possession of the phone or involved in the bomb plot, it was claimed.
According to Daly's lawyers there is even less evidence connecting him to the attack.
The case continues.