The High Court is being asked to make an attachment and committal order against Agriculture Minister Simon Coveney.
Two employees of his department, Vincent Gormley of Brownsgrove, Tuam in Co. Galway and James Scott of Glinsk, Ballymoe in Galway claim Minister Coveney is in contempt of a court order.
The two technical agricultural officers in the Department of Agriculture claim Minister Coveney has breached an undertaking about not filling two senior posts in the Department.
Lawyers for the Minister say there was indeed an undertaking, but they claim it relates solely to an external advertising process and that it has not been breached.
But this evening barrister Patrick O'Reilly for Vincent Gormley and James Scott is bringing a contempt motion against the Minister seeking a High Court order for Simon Coveney's attachment and committal.
He has told the court that it is not his clients wishes to seek the imprisonment of a government minister - the wish is that a solemn undertaking to the court is complied with.
Mr. Justice Gerard Hogan will hear the case but he has indicated it may be days before he gives a ruling.