Angus Sinclair, 67, was not present because of a medical condition when his case was called at the High Court in Edinburgh for a procedural hearing.
His defence counsel Ian Duguid QC said they wanted to look into whether what was being put forward "constitutes new evidence at all".
Sinclair was acquitted of the murders of teenagers Christine Eadie and Helen Scott at a trial at the High Court in Edinburgh in 2007, where he denied the alleged crimes.
The Crown has now made an application to bring fresh proceedings against him.
Scotland's senior law officer, the Lord Advocate, Frank Mulholland QC, told the Lord Justice Clerk, Lord Carloway, sitting with Lord Menzies and Lady Smith, that the Crown was ready to proceed to a full hearing on the issue.