A spokesperson for Ulster Bank has told RTÉ News that the bank is aware of the technical issues being experienced by customers and is working to get them fixed urgently.
The bank responded following numerous reports of customers not being able to access their bank accounts online, and unable to use their cards at tills, or withdraw money from ATMs.
RTÉ News understands that the technical problems being experienced at Ulster Bank may originate from its UK sister-bank NatWest.
It is understood that other banks have been informed of a Europe wide major technical outage at NatWest which began at 6.30pm.
NatWest is the main transaction processor for the RBS group.
It is understood that there are service level agreements in place between banks to help minimise the impact of such problems.
The Ulster Bank spokesperson said the bank was sorry for the inconvenience caused.
"We are very sorry for the system issues that affected our customers this evening. Our customers are reporting that services are coming back on line. We will confirm when all systems have returned to normal service.
"If customers have been left out of pocket as a result of these system problems, we will put this right. If any customer is unable to resolve an issue caused by the disruption, they should get in touch with our call centres or come into a branch in the morning where our staff will be ready to help," the statement added.
Messages apologising for problems were also tweeted by RBS and NatWest banks in the UK.
The problem has arisen on "Cyber Monday", the day on which the highest number of online transactions are expected in the run-up to Christmas.