A man is fighting for life in hospital after being found lying in the street with serious head injuries in Adelaide.

The 59-year-old was found at 11.30pm on Friday night in the northern suburb of Elizabeth Downs.

Emergency Services were called to Peacock Road after reports a man had been assaulted.

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He was rushed to the Royal Adelaide Hospital with life-threatening injuries, SA Police said.

Police are still searching the scene, with the attacker on the run.

"Detectives do not believe that it is a random incident," SA Police said in a statement.

Anyone with information on the incident should contact Crime Stoppers.

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