The bodies of the two men were found in two separate locations at a house in Windyhall on the outskirts of Letterkenny on Thursday afternoon.
The father, aged in his 80s, was discovered in the back of the family bungalow, while his son, aged in his 50s, was found in a car in an adjacent shed.
The two men have been named locally as Daniel Duffy and his son, Damien.
Gardai have not confirmed how the men died, but said that no firearm was used in the incident.
Both bodies have been removed from the scene and taken to Letterkenny University Hospital.
State pathologist SallyAnne Collis is to carry out the post-mortems.
Gardai said the results of the post-mortem will determine the course of the investigation.
The scene remains sealed off while the technical bureau continue to examine the scene.
The discovery at the house in the Windy Hall Road/Long Lane area was made on Thursday afternoon by a member of the public who alerted gardai.
Letterkenny councillor Gerry McMonagle, who lives close to the scene, said local people were stunned.
“I was down at the local shops this evening and I was talking to a number of people and everybody is obviously saddened and shocked that something like this could happen,” said the Sinn Fein representative.
“I think happening two days before Christmas makes it all the more shocking and sad.
“It’s tragic that two days before Christmas two family members are dead and the gardai aren’t looking for anyone else.
“People are numbed by this.
“Obviously they are thinking about the remaining family and what they are going through at this time.”
Gardai in Letterkenny have appealed for information to contact them on 074 9167100.
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Father and son found dead in a suspected murder-suicide incident in Donegal