Serial killer Mark Nash is appealing his convictions for a double murder in Grangegorman in Dublin in March 1997.
Nash, who is originally from England, has raised a number of issues about the way the trial was run.
In April 2015, Nash was found guilty of the murder of Sylvia Shiels and Mary Callanan in Grangegorman in Dublin 20 years ago.
He was arrested in August 1997 on suspicion of murdering a couple in Roscommon.
And while in custody, his trial heard he made a number of admissions in relation to the Grangegorman murders five months beforehand.
Opening his appeal today, Mark Nash's barrister Hugh Hartnett described this case as "unusual and extraordinary" because another man called Dean Lyons admitted killing the women, but died before charges were brought.
The garda investigation then hit a wall until 2009 when scientific advances led to the discovery of DNA on a jacket seized from Nash, which linked him to the Grangegorman murders.
His appeal is mostly focused on the way the judge told the jury to deal with the admissions made by Mr Lyons - as well as the possibility of cross-contamination in relation to the jacket.
The hearing is due to take three days.