Melanie Stephens, a mother of five, is thought to have suffocated Philip, five, and two-year-old Isaac before hanging herself at their home in north Wales.
Police forced their way into the property in Trawsfynydd, Gwynedd, at about 8pm on Sunday night after frantic relatives were unable to get in. A North Wales Police spokeswoman said: "Inside the property police discovered the bodies of an adult and two young children. At this early stage it is not possible to state how the occupants died."
A Home Office pathologist is conducting post-mortem examinations to establish the cause of deaths, although police say they are not treating them as suspicious.
Ms Stephens, 36, had lived at the house in Chapel Street for two years, having moved from nearby Blaenau Ffestiniog. Locals said the family seemed "happy and pleasant". Her three older children are thought to live with their father.