Iarnród Éireann cancelled the Dublin Heuston to Cork train service at 6pm on Christmas Eve.
It said this was because of 'operational problems associated with drivers not covering absences'.
It said customers would be accommodated on the 18.30 Heuston to Tralee service, with a change at Mallow for Cork.
The Cork to Dublin Heuston service at 1.30pm on Monday was also cancelled.
The company said earlier on Christmas Eve that services were running to schedule but reminded passengers that services will end at around 9pm.
A spokesperson said that 50,000 people are expected to travel on their Intercity services on Monday but that DART and commuter routes would be very quiet.
AA Roadwatch said that there were no major delays on any routes throughout the country on Monday and that traffic was quieter than usual.
Irish Ferries said their 12pm sailing of the Jonathan Swift from Holyhead to Dublin was cancelled on Monday due to conditions on the Irish Sea. However, all passengers were to be accommodated on the 2pm sailing of the Ulysses.
Transport operators say that because of the way Christmas has fallen this year, most people travelled over the weekend, resulting in lower traffic on most services.
