Angus Sinclair stood trial in 2007 accused of murdering teenagers Christine Eadie and Helen Scott. He was cleared of the charges.
The 17-year-olds were last seen leaving the World's End bar in Edinburgh in 1977.
Scotland's Lord Advocate yesterday applied to the High Court for authority under double jeopardy legislation to set aside the acquittal of Sinclair and prosecute him again.
It is the first application to be made since the Double Jeopardy (Scotland) Act 2011 came into force last November.