TSB says its systems are almost back to normal after some customers were unable to access online accounts.
Earlier, HSBC was also hit by problems with its mobile banking app, but now says all operations are back online.
TSB said: “We’re sorry for any issues our customers experienced. These services are now recovering back to normal levels.”
It is the latest in a string of IT outages for the industry, including the recent high-profile meltdown at TSB.
TSB said users of its smartphone app and internet banking had been having difficulty logging in since about 07:40 on Friday.
About the same time, HSBC said about 50% of mobile users were having trouble connecting to its app.
TSB said: “Our cards, branch and telephone services continue to operate as normal”.
An HSBC spokesman said: “An earlier issue where some customers were unable to log on to the HSBC mobile banking app has been resolved and users of the app should be able to log on as usual.
“We will be conducting an investigation into the cause of this issue, and we apologise for any inconvenience this may have caused.”
Last week, RBS, NatWest and Ulster Bank reported problems with customers unable to access their bank accounts online. Customers were locked out for about five hours.
Earlier this year, TSB’s huge IT meltdown led to weeks of pain for customers and the eventual resignation of chief executive Paul Pester.
TSB customers, many still recovering from the previous outages, were quick to vent their anger on Twitter.
“Well done @TSB on having yet another issue with online banking. Top service,” said one frustrated customer.
Said another: “So sick of the shocking online banking service currently being provided. Yet again can not access my money.”