Users of the company's online banking and mobile banking app were unable to access their accounts yesterday after a scheduled maintenance programme was not completed on time.
Some of them tweeted their frustration about the problems.
Catherine Bissett, from Bradford in West Yorkshire, said: "Ok Nationwide, no access to our accounts online or on app but would be nice if you answered the phone."
George Hoare commented: "Nationwide app needs to hurry up and work again."
Others compared the Nationwide's problems with those of RBS, which has suffered glitches with its internet banking services in the past.
One customer tweeted: "Nationwide are turning into the new RBS.
"Website problems, no access to money etc. Again underscores the importance of back-up."
A spokeswoman for the building society said customers could still withdraw cash from cash machines and make card payments.
She said the programme of work should have been over by Sunday morning and did not know why the system was not backing up and running as normal.
She added: "We apologise to our customers and are working to resolve the situation."
She pointed out the problems do not affect the building society's cash machines and people could use credit or debit cards as normal.
At the start of December last year, RBS and NatWest customers were unable to access online or phone banking services for several hours.