South Australian police were called to a property in Rosewater on Saturday afternoon.
The body of a 76-year-old woman and her 55-year-old son were found inside with significant injuries.
The bodies were discovered by the woman's daughter and the man's sister who were doing a welfare check, Acting Assistant Commissioner Graham Goodwin said.
"She came around with her daughter and they were confronted with the horrific scenes," he told reporters.
Police believe the deaths occurred in the early hours of Saturday morning.
Detectives arrested a 43-year-old man of no fixed address but who was living across the road and charged him with two counts of murder.
Police believe the man and the mother and son were known to each other, "but at this stage we don't know what that relationship was" .
Police are not seeking any other suspects and believe the incident was not random.Â
The man will face Port Adelaide Magistrates Court on Monday.
Anyone with dashcam footage or any other information is urged to contact Crime Stoppers.
"That's not only for events for today but also for events that were in the days leading up to these tragic circumstances," Mr Goodwin said.
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