Today's discussions lasted six hours and are to resume again in the morning.
As the talks adjourned, the LRC Chief Executive, Kieran Mulvey, said he could not go so far as to say progress had been made in the dispute over the company's new Belfast base, which could ground Aer Lingus flights next week.
The row centres on the pilots' refusal to train recruits for the new Belfast operation following a dispute over union negotiation rights.
Aer Lingus has threatened to suspend all pilots who continue a union ban on training from Tuesday.
The Chief Executive of the Labour Relations Commission, Kieran Mulvey, said he hopes both sides in the Aer Lingus pilots row are coming to today's talks with the intention of settling the dispute.
He said he hopes both sides will engage positively to reach positive results for both employees and the airline and added that there would be no time limit on the talks.
Mr Mulvey said it was imperative that everyone engage in solving the dispute and getting a resolution.
Assistant General Secretary of IMPACT Michael Landers insisted progress depended very much on the approach that the company takes.
He said the union had made it clear all along that it was anxious to get into talks and he said it was good that those talks were happening.
Aer Lingus Chief Executive Dermot Mannion said the airline's position had not changed and that the deadline of Tuesday remained in place.
He said the company was there to see if an end could be found to the deadlock.
Ryanair Chief Executive Michael O'Leary has said he believes that pilots at rival Aer Lingus do not have the stomach for a winter strike and that they would be back after two days if a strike occurred.
He was speaking at the annual conference of the Dublin economics workshop in Kenmare.
