It's believed the two men - aged 53 and 23 - died on Tuesday afternoon in the house they shared. Their bodies were discovered on Wednesday evening.
Neighbours told police that they had heard some noise from the house on Tuesday, but nothing out of the ordinary. After noticing that nobody had left the house on Wednesday and that a balcony door had been left open despite rain, a neighbour called round at about 10pm and discovered the body of the father in the stairwell.
When the police arrived on the scene they found the son's body. Both men appeared to have died from gunshot wounds.
Unconfirmed reports said that the son shot his father and then turned the gun on himself. Neighbours said that the pair had been heard arguing recently and that the older man's wife had moved out of the house two years ago.
"Currently we can only confirm that two men are dead - the cause of death and the exact course of events is currently the subject of our investigation," Gottlieb Türk, head of the state criminal office, said. Police sources said they did not think a third party was involved.