Unions and management at Aer Lingus resume discussions on Monday on the firm's plan to cut 1,325 jobs over the next three years.
The two sides yesterday set out their positions in a meeting which lasted for more than three hours, but they did not get into detailed negotiations.
The talks were arranged after one of the two main unions at the company, SIPTU, had threatened to hold disruptive meetings at Dublin, Cork and Shannon airports today.
Those meetings were called off after the Aer Lingus chief executive, Mr Willie Walsh, agreed to meet the unions yesterday morning.
Representatives of IMPACT, the other main union at the airline, also attended the meeting.
The two sides agreed they would make no statement on the discussions, other than to confirm that they would meet again at 8 a.m. on Monday.
It is understood, however, that the parties confined themselves yesterday to spelling out their respective positions, rather than attempting to find common ground.
As a priority, the unions at Aer Lingus want the company to lift the September 14th deadline for receipt of redundancy applications.
SIPTU says that removing the deadline would allow breathing space for "proper negotiations" on the company's restructuring plan.
As well as cutting a third of existing jobs, the company plans to outsource activities such as baggage-handling as part of its three-year business plan, designed to complete its overall transformation into a low-cost carrier.
It has also, controversially, decided to stop carrying cargo on some routes from next Wednesday.
Staff who volunteer to leave have been offered nine weeks' pay per year of service in an €80 million redundancy package.
SIPTU, however, says the terms contain "serious defects" and are not as generous as the headline figures make them appear.
A cap of 15 years, for example, has been placed on the length of service to apply in the calculation of payments.
In addition, service based on part-time and seasonal work is not to be taken into account, even though 80 per cent of employees would have been engaged in such work for significant periods before being made permanent, the union says.
SIPTU members have already balloted overwhelmingly for industrial action should the company push its plan through without agreement.
Unions also question the need for large-scale job cuts at a time when the company is line to make a profit of €100 million this year.
They are also concerned about the prospective terms and conditions for workers who remain at the airline after the restructuring plan has been implemented.
Significant pay increases for such staff are likely to be sought in the negotiations now under way.