Leo Varadkar and Micheál Martin will meet today to discuss options for forming the next government.
The Fine Gael and Fianna Fáil leaders will meet later to discuss whether there is a basis for talks on forming a historic grand coalition between the two old rivals.
Many in Leinster House think the only realistic option to form the next government will be a deal between Mr Varadkar and Mr Martin, propped up by the Greens and maybe some other smaller parties.
But there is a long way to travel between now and then.
Mr Varadkar has stressed this is just an exploratory meeting, and that he will bring word back to his parliamentary party on Wednesday if there is a basis for further talks.
Elsewhere Sinn Féin and the Green Party will start serious policy talks on a number of issues today as Mary Lou McDonald continues her efforts to form a left-wing alternative government.
