Two young brothers were discovered unhurt inside a flat with the bodies of their parents.
The two boys were found inside the top flat of Regal Court, High Street, Shanklin, on the Isle of Wight on Monday.
Post mortem examinations are due to be carried out on the man and woman, who were both in their 30s.
The woman's death is being treated as suspicious. No-one else is being sought in connection with the deaths.
The boys are now staying with a family friend, a police spokesman said.
He added: "Whilst retaining an open mind, detectives are not looking for anyone else suspected of being directly responsible for the deaths.
"The flat remains sealed off to allow for ongoing forensic examinations by specialist scenes of crime officers."
Detectives are trying to contact next-of-kin so the bodies can be formally identified.
The two children were found by a woman who works as a manager for the block of flats who was visiting the flat after concerns had been raised.
Police were called just before 1830 BST to the block of flats.
Those living and working close to the scene have spoken of their shock.
Shopkeeper Jim Isted said: "The children must have been really upset to have been in the same flat as where their parents had died.
"Everyone is really shocked, we are not an inner city here, we are not used to this sort of thing."
Neighbour Carol Rolfe said: "It's a surprise. They were just a normal, ordinary, quiet couple.
"I was in and I didn't see or hear anything."
Det Ch Insp Ben Snuggs said the investigation into the deaths was at an early stage.
- 9 August 2010