Mark Lundy's lawyer says his client is a victim of flawed science

Mark Lundy's last-ditch attempt to appeal his double-murder convictions begun in the Supreme Court on Tuesday.

Lundy was twice found guilty of murdering his wife and daughter in 2000 but his lawyer says he's a victim of flawed science and he deserves another trial.

They are fighting to overturn the Court of Appeal's decision to deny him a third trial - despite dismissing key evidence used against him in his 2015 re-trial.

This week marks the 19th anniversary of the murder of Christine and Amber Lundy in their Palmerston North home.

Husband and father, Mark Lundy, has twice been convicted of their murders. He was first convicted in 2002, then again at his 2015 re-trial

At the heart of the Crown's case is the presence of brain or spinal cord tissue on Lundy's shirt, which it argued belonged to Christine Lundy.

Something called messenger RNA analysis was used to determine the tissue was more likely human than animal.

That was the crux of today's hearing because, after the retrial, the Court of Appeal ruled mRNA was inadmissible.

However, the Court dismissed Lundy's appeal because it found he did still receive a fair trial and the guilty verdict was inevitable because of other evidence. The Supreme Court will determine whether that decision was correct.

The Crown today focused on its other scientific evidence - that Christine's DNA was also found on her husband's shirt, as was brain or central nervous system (CNS) tissue.

Crown lawyer Philip Morgan QC says the mRNA wasn't vital.

"There were two key bits evidence - CNS and DNA and everything else was an add on," he said.

The case will continue in the Supreme Court on Wednesday.