The Supreme Court will hear the appeal by former Rehab CEO Angela Kerins against the High Court's rejection of her case against the Dáil's Public Accounts Committee in March.
A week later, the court will hear businessman Denis O'Brien's appeal against the dismissal of his action over statements made by two TDs in the Dáil about his banking affairs.
Both appeals raise similar issues relating to the separation of powers and the courts' ability to intervene in decisions and proceedings in the Oireachtas.
The Supreme Court has decided they should be heard in sequence.
The court has allocated five days for Ms Kerins' appeal from 13 March and two days for Mr O'Brien's from 20 March.
Ms Kerins claimed two hearings by the PAC in February and April 2014, were a "witch hunt" against her.
The PAC argued it was entitled to scrutinise how public funds were spent as around €80 million in public monies were paid annually to Rehab companies.
The High Court found that because the Constitution conferred absolute privilege on what was said in the Oireachtas and the PAC made no determination against her, the courts could not intervene in how the hearings were conducted.
Mr O'Brien is appealing the High Court's judgment dismissing his case against the Dáil over statements made by Social Democrats TD Catherine Murphy and Sinn Féin TD Pearse Doherty about his banking affairs.
The High Court found in that case that what Mr O'Brien sought was prohibited by the separation of powers under the Constitution and would have a "chilling effect" on parliamentary speech into the future.
