The case was launched by businessman and founder of the New Beginnings group David Hall, of College Grove, Castleknock, Dublin.amounting to €31 billion to bail out the banks
The court's heard the promissory notes represent 'a blank cheque' to financial institutions IBRC, EBS and Irish Nationwide.
David Hall claims the issuing of the notes is unlawful as it is not subject to a Dail vote.
He's trying to stop the State paying the IOUs which amount to €31 billion.
Lawyers for the finance minister says his argument is based on a misapprehension of the procedures for approving expenditure and borrowing by the State.
Mr Hall's legal standing to take the case was also questioned as he's not a member of the Dail.
3 deputies, Indpendents Shane Ross and Stephen Donnelly, and People Before Profit's Joan Collins, turned up to let the court know they were supporting David Hall.
High Court President Nicholas Kearns is to give a ruling today.
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