Both banks released statements at around 10.25am on Saturday.
It comes after Friday nights online banking issues with NatWest, RBS, Lloyds and Halifax.
Some NatWest customers said cash appeared to have disappeared into thin air as attempts were made to transfer money.
The glitches came on what was payday for many people, being the last Friday of the month, and a day when many were checking their finances as they made preparations for the bank holiday.0
RBS, which includes NatWest in its brands, said some customers had experienced problems with its mobile banking app and with online banking running slowly.
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