Family members of the victims gave each other the thumbs up when the ACT Court of Appeal on Monday upheld McDougall's two life sentences for the murders of Struan Bolas, 48, and Julie Tattersall, 35, at a Downer home in 2008.

In 2011, McDougall became the first person to be found guilty of murder in the ACT for more than a decade.

But he appealed against his conviction and sentence for the murder of Mr Bolas on two grounds.

Defence lawyers argued that trial judge Malcolm Gray erred in finding McDougall did not act in self-defence and failed to properly explain his reasons.

McDougall also appealed against the life sentence imposed for the murder of Ms Tattersall, but his counsel, Peter Hastings, QC, told the court that challenge was contingent on the success of the first appeal.

McDougall murdered the pair after the trio had been drinking for a number of hours at Mr Bolas' home in September 2008.

The court heard the atmosphere became heated when the conversation turned to the topic of police informants.

McDougall claimed Mr Bolas attacked him with a cleaver, but was disarmed and he was repeatedly hit with the weapon.

McDougall, who was 34 at the time, then turned on Ms Tattersall before setting the house alight by stuffing paper in the toaster. He later dumped his bloodied clothes at the Mugga Lane tip.

Mr Hastings told the three appeal court judges - Justice John Burns, Justice Richard Refshauge and Justice Hilary Penfold - at an October hearing that their client's frenzied attack was not the work of a rational man.

He argued his client was "partly deranged" when he attacked his first victim with a meat cleaver and had thought he was in a "fight to the death".

The defence said the conviction amounted to a miscarriage of justice.

But the three judges dismissed the appeals and Justice Refshauge published the reasons on Monday.

The judges found that it was open to Justice Gray to make the findings of facts that he did concerning the death of Mr Bolas.

"His Honour correctly identified the law relevant to the issues raised at trial, and in particular the law relevant to self-defence," the three judges wrote.

"His Honour's reasons sufficiently identified the process of reasoning by which he found the facts and applied the law to the facts as found, and concluded that the appellant was guilty.

''The appellant's appeal against conviction and sentence for the murder of Mr Bolas must be dismissed.''

Subsequently, the appeal against sentence for the murder of Ms Tattersall was also dismissed "as the appellant made it clear that it was only to be pursued if his appeal against conviction for the murder of Mr Bolas was upheld".