A media think tank has called for the BBC to sell off Radio 1 and 2 "as soon as possible".
Terry Wogan's Radio 2 show draws the BBC's biggest radio audience
The BBC's annual radio budget of £450m had severely limited growth in the commercial radio sector, the European Media Forum (EMF) report said.
As the two rely mainly on music they have a limited public service role - a factor which strengthens the case for privatisation, it added.
The EMF estimated the BBC could raise more than £500m through a sell off.
"Our argument is that whereas you can put forward a pretty compelling case for a public sector role for Radios 4 and 3 - and also Radio 5, it gets a bit thin when you look at Radios 1 and 2 - and they could survive quite easily in the private sector," said the report's author, economist Keith Boyfield.
The report argued that the UK radio sector was suffering from "stunted growth", and the problem had been intensified by the BBC's ability to cross promote and cross subsidise across a number of media platforms.
The EMF also argued that Radios 1 and 2 would fare well in the commercial sector as the stations currently attract the highest radio audiences in the UK.
"If both Radio 1 and 2 were sold in a combined sale the proceeds might arguably total £500m or more," it added.
But the BBC said both radio stations offered diverse music, documentaries and current affairs shows that could not be found in the commercial sector.
It said the stations provided innovative and challenging content that the market would not otherwise provide.
Kelvin MacKenzie, former chief executive of the Wireless Group which controls a number of UK local radio stations, welcomed the EMF's privatisation call as a "splendid idea".
The wide availability of commercial music on radio, the internet and through downloads meant that the two stations could no longer lay claim to offering a public service as set out in the BBC's remit, he said.
"Why does the BBC want to hang onto basically what is, on Radio One, pop music, and on Radio 2, middle of the road music, when all they're really doing is bankrupting commercial forces?," he told Radio 4's Today programme.
Commercial radio is currently going through a "nightmare" which is made worse by the fact that the BBC has a 60% share of the radio audience, Mr MacKenzie said.
"Why should advertisers go to commercial radio when they're missing 60% of the audience?" he added.
The report came as Chrysalis - which owns the Heart and Galaxy brands - blamed a tough advertising market for a sharp 46% drop in full year profits to £2.1m.
Earlier this year, radio broadcaster GCap Media blamed falling audiences and short advert breaks for a 17% drop in revenues in the first three months of the year.