Lawyers for Michael McKevitt and Liam Campbell have based the challenge on their inability to cross-examine an FBI spy whose evidence was central to the case against them.
They are also contesting the decision to allow hearsay evidence from David Rupert in the action brought by relatives of some of the 29 people killed in the atrocity.
The disclosure comes as two other men originally held responsible, Colm Murphy and Seamus Daly, prepare to face a retrial at the High Court in Belfast.
No-one has been criminally convicted of the Real IRA bomb attack that devastated the Co Tyrone market town in August 1998.
But McKevitt, a convicted Real IRA leader serving a 20-year jail sentence; Campbell, a farmer from Co Louth currently fighting extradition to Lithuania over gun smuggling allegations; Murphy, a Dundalk-based builder and publican; and Daly, from Culaville, Co Monaghan, were all held liable for the bombing in a civil ruling in 2009.
Mr Justice Morgan, who is now Northern Ireland's Lord Chief Justice, ordered them to pay £1.6m in compensation.
The Court of Appeal subsequently upheld Murphy and Daly's challenges to the verdict and ordered them to face a retrial which gets underway next week.
However, McKevitt and Campbell failed to overturn the rulings against them.
A further petition to the Supreme Court in London was also rejected, leaving them with one final option of seeking to go to Europe.
Legal papers prepared on their behalf focus on the role and credibility of Rupert, an American trucking boss-turned FBI spy who infiltrated dissident republican ranks.
He is on a witness protection programme after testifying for the prosecution at the criminal trial of McKevitt in Dublin in 2000.
Although Rupert was forbidden from attending the original civil action because of health and security reasons, more than 900 emails between the spy and his handlers were submitted as evidence.
The lawyer representing McKevitt and Campbell have objected to that move.
Kevin Winters confirmed: "Having exhausted all domestic court processes both of my clients have lodged applications with the European Court of Human Rights.
"The key areas that the court will be asked to look at is the reliance on the hearsay evidence of David Rupert, and the inability to cross-examine him about his claims."
Papers lodged on behalf of the pair will undergo a preliminary assessment of the points raised.
It is expected that the European Court of Human Rights will make a provisional ruling on the merits of each application by July.