A 67-year-old man was remanded for custody of two UDR soldiers following his extradition from the Republic of Ireland.
John Downey appeared on Saturday in front of the Omagh Magistrates Court.
Downey was arrested for the first time in October 2018 in the Republic of Ireland under a European arrest warrant.
He fought extradition, but lost his last appeal and handed over to the Irish police Gardaí on Friday.
Downey is wanted by the prosecutor in connection with the killings of UDR soldier Alfred Johnston, 32, a father of four children, and James Eames, 33, a father of three children.
Both were killed in 1972 in a bomb attack in Enniskillen.
Downey is also accused of helping with an explosion.
Before the hearing, a lot of supporters, including representatives of Sinn Fein, gathered in court.
& # 39; flight risk & # 39;
A detective chief inspector told the judicial police that she was going to appeal for a bail, considering Mr Downey to be a flight risk.
He referred to the repeated attempts of the defendant to appeal against the extradition order.
"According to the police, the defendant is not ready to face the judiciary," he said.
In 2013, Downey was accused of murdering four men of the Royal Household Cavalry in a bomb attack in London's Hyde Park in 1982.
The case collapsed dramatically after it became known that the defendant had an assurance from former Prime Minister Tony Blair that he was not actively sought by the authorities.
In court on Saturday, the Detective Chief Inspector announced that the families of those killed in the incident had opened a civil suit against Mr. Downey in 2014 following the collapse of the Hyde Park bombing case.
He informed the court that Mr Downey had subsequently transferred assets, including land, from his name to his wife's name.
A solicitor acting on behalf of the defendant stated that his client had amicably transferred to Gardaí and fully complied with the previous bail conditions in 2013 and 2014.
"Long and tedious"
He described the land transfers as "red herring" and said his client was a sick man.
Judge Michael Ranaghan said he sees a "lengthy" trial.
He found, however, that the defendant was a flight risk and the bail was denied.
The judge told Mr Downey that he could appeal his decision to the High Court before he would appear in court on 25 October.