Lawyers for deceased politicians under investigation by the tribunal are seeking an end to investigations into their clients on the basis that it cannot fairly inquire into someone who is dead.
The family of the late Fine Gael councillor, Tom Hand, will seek to end the tribunal's inquiries into their father in a legal submission next week.
This stance is likely to be supported by the families of two deceased Fianna Fáil councillors, Jack Larkin and Cyril Gallagher, also implicated in allegations currently before the tribunal.
Mr Cormac Ó Dúlacháin, for the family and estate of Mr Hand, said the tribunal should discontinue its inquiries into Mr Hand because it was incapable of discharging a duty of carrying out a full and fair inquiry into him.
He said the way the tribunal was organising its business rendered an unfairness and a "lack of fullness" to its inquiries into Mr Hand.
He pointed out that the tribunal had referred in correspondence to the assets that Mr Hand may have obtained during his lifetime and the distribution of assets after he died.
Counsel said he was entitled to an interpretation of his clients' rights in these matters.
Issues arose in the context of a deceased person against whom allegations had been made. These issues had not been explored fully by any other tribunal.
Up to now, such matters had been considered by reference to a narrow interpretation of defamation law, which excluded libel actions by dead people, he said.
Mr Justice Flood invited Mr Ó Dúlacháin to make a written submission to the tribunal by next Monday.