Senior counsel for relatives of those murdered in the atrocity claimed Colm Murphy and Seamus Daly played central roles for which they should be held liable.
Lord Brennan QC also challenged the two men to come to court and testify over the alleged telephone links.
Without an explanation the evidence of their alleged involvement in the Real IRA attack is compelling, he contended.
Murphy, a Dundalk-based builder and publican; and Daly, from Culaville, Co Monaghan, are being sued over the August 1998 outrage which killed 29 people and injured hundreds more.
Both men deny the claim against them.
They were ordered to face a civil retrial after their appeals against being held liable for the bombing were upheld.
Two other men found responsible 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.
Neither Murphy nor Daly was present as the new hearing got underway in Belfast, nor were any of the families who brought the action against for the opening of a case expected to last six weeks.
Setting out their claim, Lord Brennan told Mr Justice Gillen that the operation to transport 500lb of explosives into Omagh was a determined and organised crime carried out by committed terrorists.
At least two cars had to be involved in the cross-border bomb run - one carrying the device and another used as a scout the route, he submitted.
Phones with roaming facilities which would enable them to work both in the Republic and Northern Ireland were regarded as essential to the operation.
It is for Mr Murphy and Mr Daly to explain to Your Lordship in due course, if they give evidence, how did these telephones which they had in their ownership or possession, come to be used in a bomb run when lo and behold they were back in their possession at the beginning of the next week.
Lord Brennan QC
Lord Brennan contended: "Those who provided such mobile phones for such use and those who used them in a bomb run were playing a central role in the commission of this crime.
"As well as owning the Emerald Bar in Dundalk at the time of the bombing Murphy also ran a construction firm whose employees included Daly and another man, Terence Morgan," the court heard.
Detailing telephone evidence surrounding the attack, Lord Brennan argued that Murphy provided his own mobile, ending in 585, which was registered to him and a second mobile that he had borrowed from Terence Morgan over the weekend of the bombing.
"His liability arises with the use of either or both."
According to the barrister Daly can also be connected due to a call he is alleged to have made shortly after the explosion.
"The defendant Daly used the phone 585 during the bomb run and by doing so demonstrated that he was a participant," he claimed.
Lord Brennan argued that the defendants were well connected through work and socially.
"These people knew each other, these are not phone calls being made in some vacuum," he said.
The hearing will focus on the defendants alleged liability, rather than contesting the level of damages set at £1.6m in the original verdict.
Lord Brennan contended that the onus was on the two men provide answers over the alleged telephone links to them.
The court heard how Murphy provided a lengthy and detailed alibi during questioning by gardai six months after the bombing.
He claimed to have been in the Emerald Bar drinking on the day at the attack.
At one point he stated: "I was never in Omagh in my life."
But based on phone records, Lord Brennan insisted that if Murphy gives evidence he has a choice of saying either he was using his mobile or he gave it to someone else.
"Here is a man with very careful recollection. He can remember that kind of thing six months after the event," the barrister pointed out.
"The court will be surprised he he gives evidence and becomes vague about his evidence."
He added: "If he has no rational explanation... then he was either in the bomb run or he gave it to someone for use in the bomb run."
The hearing continues.