Neither Mr Kenny, Micheal Martin, Gerry Adams or Richard Boyd Barrett secured enough votes from TDs to become Taoiseach.
The Dáil has now been adjourned until the 22nd of March, when there will be an update on talks to form a Government.
Enda Kenny travelled to Aras an Uachtarain and resigned last night.
He says he's got a busy agenda in his role as caretaker Taoiseach.
