Judges are expected to rule before the end of the month if British soldiers should give evidence in person to the Bloody Sunday tribunal.
The Saville Inquiry into the murder of 14 civilians in Derry in January 1972 resumes today after a three-week break.
The hearing at the Guildhall has ruled paratroopers involved on the day should take the stand.
But lawyers for the soldiers argue they should not be ordered to come to the city for their own safety.
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Following the hearing in the High Court Lord Justice Rose and Mr Justice Sullivan are expected to make their judgment within the next two weeks.
An application for anonymity by witness X is to be heard tomorrow.