The family of bankrupt businessman Sean Quinn has said the Commercial Court has an inherent power to lift a statutory stay on their lawsuit against IBRC.
The stay took effect when the Oireachtas enacted emergency legislation last month to wind up IBRC.
The act halts existing legal proceedings but does not stop new cases being brought against the bank.
The Quinns' lawyers said the distinction is "arbitrary" and "invidious".
They said their bid to overturn the stay is "somewhat unique" as the special liquidators appointed to IBRC agree with their position.
The Quinns' case was initiated in 2011 and centres on a challenge to the legality of €2.3bn of loans issued to their businesses by the former Anglo Irish Bank.