The victims’ lawyers have said it will be the first time Adams will be cross-examined in an English court about his alleged leadership role in the IRA.
The judge will rule on the issue of liability “on the balance of probabilities”.
The action commenced in 2022, just before the Legacy Act banned new civil claims related to the Troubles, although this is in the process of being reversed.
The claimants have raised more than £100,000 through crowdfunding to bring the case.
They said they were acting not just for themselves, but for all IRA victims.
As a result of a pre-trial ruling, Adams is unable to recover his legal costs from the claimants, believed to be six figures, should he successfully defend the action.
The IRA was responsible for around 1,700 killings during the Troubles.
Adams was once charged with IRA membership in 1978, but the case was dropped due to insufficient evidence.
His only Troubles-era convictions, for twice attempting to escape prison while interned without trial in the mid-1970s, were quashed in 2020.
He has been questioned in court before about his alleged IRA past – at the Ballymurphy inquest in Belfast in 2019 and during a libel case against the BBC in Dublin last year.