The Swiss Competition Commission, known as Comco, said a raft of banks ran cartels to influence rates dating as far back as 2005.
As well as RBS and Barclays, Comco also fined US investment banking giants JP Morgan Chase & Co and Citigroup, German group Deutsche Bank, French player Societe Generale and Swiss bank Credit Suisse.
It marks the latest in a long line of bank penalties for rate-rigging scandals that have come to light since the 2008 global financial crisis.
Vincent Martenet, President of Comco, said: “It is a big sanction based on an in-depth investigation.”
Just weeks ago, the European Commission announced fines totalling 485 million euro (£409 million) for HSBC, JPMorgan and Credit Agricole for the part they played in conspiring to rig interest rate derivatives.
Comco said taxpayer-backed RBS and JP Morgan ran a “bilateral cartel” to influence the Swiss franc Libor benchmark rate between 2008 and 2009.
RBS avoided a penalty as it was given immunity for revealing the cartel, while JP Morgan was fined 33.9 million Swiss francs (£26.8 million). But RBS was fined by Comco for its role in rigging other financial rates and it was part of a group alongside Citigroup, Deutsche Bank, and JP Morgan who will pay a total of 14.4 million Swiss francs (£11.4 million) for colluding to influence the yen Libor rate and between 2007 and 2010.
The commission is continuing a related investigation of banks and dealers including Britain’s Lloyds Banking Group and HSBC.
RBS and Barclays were among another group of banks fined £35.8 million for manipulating the Euro Interbank Offered Rate, or Euribor.
Deutsche Bank and Societe Generale also took part in this cartel between 2005 and 2008, according to Comco, but Deutsche Bank was not fined as it blew the whistle on the arrangement. The proceeding continues against HSBC, BNP Paribas, Credit Agricole, JP Morgan and Rabobank. The commission said RBS was involved further - alongside Credit Suisse, JP Morgan and UBS - in fixing the price of Swiss franc interest rate derivatives in 2007.
UBS received immunity for revealing the cartel and was not fined, but the other players will have to pay £4.3 million. Interbank lending rates are used to set billions of financial trades and deals worldwide every day.