Relatives of four soldiers murdered by an IRA bomb in Hyde Park in 1982 are seeking damages from the main suspect.
The four members of the Royal Household Cavalry were killed as they rode to the Changing of the Guard ceremony in Whitehall on 20 July 1982.
A criminal case against John Downey, who denied four counts of murder, collapsed in controversial circumstances in 2014.
The civil action is taking place in London and is due to last three days.
It emerged that, by mistake, Mr Downey had received an assurance from the government that he was not wanted in connection with any offence.
The so-called “On-the-Run” letters were issued as part of the Northern Ireland peace agreement in 1998.
The judge ruled the letter guaranteed Mr Downey would not face trial and that to proceed was an abuse of executive power.
Dismayed by the outcome, the daughter of one of the soldiers launched civil proceedings, similar to a landmark case brought in 2009 by relatives of those killed in the 1998 Omagh bomb.
The victims of the Hyde Park attack were Squadron Quartermaster Cpl Roy Bright, 36, Lt Dennis Daly, 23, Trooper Simon Tipper, 19, and L/Cpl Jeffrey Young, 19.
They died when a bomb planted in the boot of a car was detonated by remote control as they rode past.
Seven horses were also killed and 31 people injured.
Civil cases have a much lower burden of proof than in criminal prosecutions, with a judge reaching a verdict based on the balance of probabilities.
Mr Downey is currently remanded in custody at Maghaberry Prison in Northern Ireland facing other charges.
The 67-year-old from Creeslough in County Donegal is accused of murdering two UDR soldiers, Alfred Johnston and James Eames, in an IRA bomb attack in Enniskillen in 1972.
Who are the On the Runs?
The Northern Ireland Good Friday Agreement of 1998 meant anyone convicted of paramilitary crimes was eligible for early release.
However, this did not cover those suspected of such crimes, nor did it cover people who had been charged or convicted but who had escaped from prison.
Negotiations continued after the signing of the agreement between Sinn Féin and the government over how to deal with those known as On the Runs.
Sinn Féin sought a scheme that would allow escaped prisoners and those who were concerned they might be arrested to return to the UK, but a formal legal solution proved difficult to establish in the face of strong unionist opposition.
Against this backdrop, the IRA had still not put its weapons beyond use and Sinn Féin needed grassroots republicans to continue supporting the peace process.