The couple, named locally as Ken and Donna Graham, were discovered in a house in Echline Gardens, South Queensferry, near Edinburgh, at about 5pm yesterday.
The deaths are being treated as unexplained, police said.
Detective Chief Inspector Gary Cunningham, who is in charge of the investigation, said: "This is a tragic event and our thoughts are with the immediate family and friends of the victims.
"We still have some investigations to carry out, and police are likely to be in the area for the next few days, however I can confirm that we are not looking for anyone in connection with these deaths."
Police cordoned off part of the street to examine the scene and officers have been carrying out door-to-door inquiries in the area.