The body of Malcolm Ballantyne, known as Malky, was found at his home in Glebe Place by a family member shortly after 13:00 on Friday.
A post-mortem examination is taking place but police are treating the death as suspicious.
Officers are trying to trace Mr Ballantyne's movements on Thursday and Friday and are also checking CCTV.
Det Ch Insp Gary Cunningham said: "Malky was found yesterday by a family member who is obviously distraught at what has happened.
"He is a well-known character in the area and has a routine where he visits and socialises in various pubs in Stevenson most days - generally in the morning.
"We are keen to find out if anyone saw Malky between 1000 hours on Thursday 20 August and 1300 hours on Friday 21 August."
Door-to-door inquiries are taking place in Saltcoats and Stevenson and there are extra uniformed patrols in the area.
Investigations are under way after the death of 72-year-old man at a flat in Saltcoats, in North Ayrshire.