Irish Rail says its service is subject to line inspections
Several transport companies are updating customers in the wake of Storm Ophelia.
Dublin Bus says services will resume on Tuesday morning.
The company earlier said services were suspended on Monday from 10.00am to 6.00pm due to the storm.
It had hoped to return to normal service after that.
But it says due to updated information received from Met Éireann and the National Emergency Coordination Committee, Dublin Bus was "not in a position to resume services" on Monday evening.
It says it expects services will resume from the first bus on Tuesday morning, October 17th.
Bus Éireann says it will resume all services, apart from the School Transport Scheme, on Tuesday - but some disruption is expected.
This will include all Bus Éireann services, the Expressway network, Eurolines and GoBÉ services.
However, the company expects disruption to some services in areas where the worst damage has been caused by the storm.
It says this could include diversions, delays or cancellations.
While the Luas operator says there will be no Red or Green Line services on Tuesday morning.
This is due to an incident on Monday in the Luas depot at Red Cow.
A technical room was damaged because of Storm Ophelia.
Luas says: "It will take time to investigate the damage caused and time to repair. We are not able to give an estimate in relation to the time it will take."
The situation will be reviewed at midday on Tuesday.
Irish Rail say it expects services to resume on Tuesday, subject to line inspections.
Iarnród Éireann earlier cancelled all services after 2.00pm on Monday.
All services into and out of Connolly Station were suspended, as well as services into and out of Heuston.
The last DART service ran at 2.00pm, and all Commuter and Intercity services also ceased.
While it expects operations to resume on Tuesday morning, it says there will be some minor service alterations and capacity reductions.
05.50 Cork to Dublin Heuston cancelled, 06.15 Cork to Dublin Heuston will additionally serve Mallow, Charleville and Limerick Junction.
Limerick to Ballybrophy via Nenagh services cancelled. Bus substitution in place.
09.45 Westport to Dublin Heuston cancelled.
Reduced capacity on 05.30, 06.40 & 07.40 Limerick to Dublin services
Reduced capacity on 05.30, 06.30 & 07.30 Galway to Dublin services