Eugenios and Hilda Marcel died 23 and nearly 30 years ago respectively, but their bodies were kept at a private mausoleum by their sons Nigel and Melvyn.
Their bodies have been in Edinburgh City Mortuary, run by the Edinburgh council, since being discovered in the basement of a former fishmonger’s in 2002.
It was reported that staff at an undertakers in West Lothian had been paid to preserve the bodies by embalming them, and four employees were sacked.
But no charges were ever brought.
Now Edinburgh City Council is due to appear at the Court of Session at the end of this month to continue its bid to win the legal authority to lay the bodies to rest.
Local authorities can normally cremate or bury unclaimed bodies in their custody and indeed have a legal obligation to dispose of them properly.
But Edinburgh City Council had great difficulty in making any progress in negotiating with the two sons as they had left the country, leaving only a forwarding address.
The local authority had been intending to resolve the matter some time ago, but has had to wait for the Court of Session to accommodate different dates for the case.
A council spokeswoman said: “This matter is scheduled to appear before court again on January 23 and the council will await its decision.”
Jeremy Balfour, Conservative list MSP for Lothian and a serving Edinburgh city councillor since 2005, said there the council had not been to blame for this unfortunate saga.
He said: “This needs to be dealt with as soon as possible and bring this issue to an end. We have to do that in respect of those who have passed away.”
Embalming a body helps to slow down the natural process of decay after death and to help the skin keep as natural a colour as possible.
A spokesman for the National Association of Funeral Directors said families would choose to embalm a body to preserve it as well as possible prior to a funeral.
He said: “Not all funeral directors offer the service, but it can be particularly useful when there is a delay in a funeral.”
He added that some funeral directors also choose to embalm wherever possible to assist staff in looking after the body as part of their overall care.