Customers cannot currently access the banks' customer home pages to link to online banking.
The website Downdetector.co.uk said the outage for both sites occurred shortly after 9am on Tuesday.
NatWest issued a statement on Twitter saying it was working to fix the problem.
RBS also said the website was out of service.
The banks, which are both owned by NatWest Holdings, have some 25 million customers between them.
A spokesman for the banks said: "We are aware that customers are currently experiencing issues accessing our websites and online banking login pages. We apologise for the inconvenience caused. We are aware of the problem and are working hard to fix it.
"Customers can still access online banking via direct links, they can use their mobile app, ATMs, telephone banking, or visit their local branch."
The outage is the latest in a string of IT problems for both banks this year.