Kathleen and Jimmy Cuddihy, who were in their 70s, were found dead just outside Carndonagh on 22 October 2014.
Their son, Julian Cuddihy, appeared at Dublin's Central Criminal Court on Tuesday.
The court heard he admitted killing his parents but the jury must decide his mental state at the time.
Counsel for the prosecution told the jury that forensic psychiatrists for both the prosecution and the defence are in agreement and will give evidence that Mr Cuddihy was suffering from paranoid schizophrenia at the time.
The psychiatrists will also say that Mr Cuddihy, who was 42-years-old at the time, believed he was carrying out his parents' wishes and was helping them to secure a place in heaven.
The jury heard evidence from a post-mortem examination that the couple had severe head injuries.
The court was told that an axe and scissors were found at the scene.
Julian Cuddihy was arrested a short time later after it became known he had taken his father's car to a lake area near Clonmany.
The court heard that after his arrest, Mr Cuddihy asked gardai (Irish police) if they were telling him his parents were dead.
Mr Cuddihy has been receiving treatment at the Central Mental Hospital in Dundrum since his arrest.
The trial continues.

Hastings Pier is being rebuilt with £14m of money raised mainly through the Heritage Lottery Fund.
It is now hoped a further £300,000 can be raised by selling 3,000 shares for £100 each.
The charity behind the restoration said investors would have a say in the pier's future.
The 140-year-old structure was almost completely destroyed by fire in October 2010.
Simon Opie, CEO of the Hastings Pier Charity, said the shares were important to continue interest in the pier after its restoration.
He said: "[The shares] are not just about the money, but it is about creating shareholder members, people who are invested in the pier, people who care about the town, the heritage of the pier, and people who will be here for the long term.
"The money that we have raised will restore the pier but beyond that it needs to have an economically viable future and that's what we hope we will create."
The Panamanian company Ravenclaw, which owned the pier, was issued with a compulsory purchase order after it failed to carry out repair work.
The order was granted in 2012 and the council formally took ownership of the pier in August.
It is hoped the restoration will be completed by spring 2015.
Hastings Council leader, Jeremy Birch, said: "This is the people's pier so let them have a stake in it."
The shares will go on sale on Saturday through a community shares website.

Livi's 2-0 win over their nearest challengers came courtesy of goals from Dale Carrick and Nicky Cadden.
Brechin City moved above Alloa Athletic and to within a point of second place by beating Stranraer, with the Wasps drawing with Queen's Park.
East Fife won Barry Smith's first match in charge against Peterhead and bottom side Stenhousemuir beat Albion Rovers.
Carrick's shot gave Livi an early lead at home to the Diamonds and Cadden's late strike sealed the win for David Hopkin's side.
At Glebe Park, Ally Love fired Brechin ahead on the quarter-hour and that lead was doubled by Connor McLennan's free-kick before half-time.
Stranraer had Steven Bell sent off in the second half for two bookings.
Queen's Park went ahead away to Alloa through Ross Millen's 62nd-minute shot, but the hosts were level within seven minutes through Greig Spence's strike.
The Fifers moved out of the bottom two after scoring two second-half goals against Peterhead, Jason Kerr then Kevin O'Hara firing in.
Smith's side were replaced in ninth by Stranraer, who are only two points ahead of Stenny.
Willis Furtado's strike gave the Ochilview side a narrow home win.
A man has pleaded not guilty by reason of insanity to the murder of his parents at their home in County Donegal almost two years ago.
[NEXT_CONCEPT]
Shares in a derelict seaside pier that was almost destroyed by fire three years ago will be offered to the community to aid its restoration.
[NEXT_CONCEPT]
Livingston moved 10 points clear at the top of Scottish League One after beating Airdrieonians.