The Crown Office has confirmed police have been instructed to carry out further investigations into Angus Sinclair and the 1977 killings, with the families of the victims, who were just 17 when they died, being kept informed of developments.
Christine Eadie and Helen Scott were last seen alive in the World's End pub on Edinburgh's Royal Mile. They were found strangled and bound six miles apart in East Lothian countryside the day after their disappearance.
They had been beaten and raped and there was no attempt by their killer to conceal the bodies, which were found in open fields.
Sinclair, a convicted killer and sex offender who is serving a life sentence for killing 17-year-old Mary Gallagher in November 1978, was acquitted in 2007 of the World's End murders after the judge dismissed the case. Lord Clarke said the Crown had insufficient evidence to proceed.
It is now believed fresh forensic evidence has emerged that could send Sinclair back to the dock. The Crown can apply within a matter of weeks for the acquittal to be set aside.
Morain Scott, 81, the father of Helen, said last night of the development: "Obviously, I have got to be highly optimistic after all this time but it is up to the Crown and the police, really.
"All I want is justice for the girls, for Helen and Christine. If I have got to go into a courtroom again, I have got to go into a courtroom.
"The pain never goes away and that is a definite. Every day that I see something on the news I think of the parents and think what the parents have got to go through."
Mr Scott, of Edinburgh, said it was his wish to see justice within his lifetime.
"I always said to my wife before she died that I would get justice," he said.
Elish Angiolini, then Lord Advocate, was forced to defend the Crown's failed prosecution at Holyrood.
A number of cases are under review by the Crown following the introduction of the new double jeopardy legislation in November last year.
The collapse of Sinclair's trial was a main driver in the review of the legal position on trying an accused for a second time for the same crime. A spokesman for the Crown Office said: "Whilst it is not appropriate to comment or speculate on the live investigation into these murders, the public can be assured that where there is new, compelling evidence of guilt, the length of time since committal or acquittal should offer no protection.
"We are committed to using the powers under the new double jeopardy legislation; we hope that this commitment will give reassurance to the families of Helen Scott and Christine Eadie."
Following the new legislation, police and prosecutors are also working to bring a fresh case against those acquitted of the murder of Indian waiter Surjit Chhokar in Overtown, Lanarkshire, in 1998.