A post mortem investigation is taking place at Flax Bourton, in Bristol today, into the death of 36 year old Graham Anderson.
Mr Anderson's body was discovered on Saturday along with the bodies of his two sons, aged 11 and 3.
They were found in a flat in Tidworth by the Landlady, who was about to show prospective tenants around the property.
Detectives aren't looking for anyone else in connection with the deaths - but are keen to hear from anyone who saw Mr Anderson with the boys, particularly using buses in the last few days.
Detective Chief Inspector Ian Saunders from the Brunel Major Crime Investigation Team, who is leading the investigation into the deaths, said: "I am extremely keen for any sightings of Graham Anderson with the two children between Saturday 25 August and Saturday 1 September.
"He was a regular bus user and I now need to trace his movements, and those of the boys during the week leading up to the discovery of their bodies at lunchtime yesterday."
The post mortem examinations into the two boys, who were aged 11 and 3, are likely to be conducted over the next couple of days in Southampton.
Anyone who has information that may assist police is asked to call Wiltshire Police on 101 and ask for the incident room, or if they wish to remain anonymous they can call Crimestoppers on 0800 555 111.