The bodies of Jimmy and Kathleen Cuddihy were found at their home in Carndonagh shortly after 9 o'clock this morning.
The man was subsequently arrested and is being questioned at Buncrana Garda Station.
The state pathologist Dr Marie Cassidy has arrived at the scene to carry out a preliminary examination.
A hatchet found at the house is also to be examined as part of the investigation.
These local people have been giving their reaction to our reporter Barry Whyte: