Lord Hamilton will decide whether the documents should be handed over
Legal debate has taken place behind closed doors to try to resolve a long-running row over secret documents linked to the Lockerbie bombing appeal.
The man convicted of the atrocity, Abdelbasset al Megrahi, 56, believes they could help to clear him.
UK Foreign secretary David Miliband said handing them to defence lawyers would put national security at risk.
Judges now have to decide whether Megrahi can get a fair appeal hearing without access to the papers.
Scotland's top judge, Lord Hamilton, sitting with Lords Kingarth and Eassie, will make a ruling on the matter.
It is the first time the Scottish courts have had to deal with such a question.
Megrahi is currently serving a life sentence for the 1988 bombing, in which 270 people died.
He has already lost one appeal against conviction, but the Scottish Criminal Cases Review Commission said he should have another.
It has seen the secret documents and said they should have been shown to defence lawyers before Megrahi's trial.