A woman has died and a man is fighting for his life in hospital after their car hit a tree on a major highway.

The man was behind the wheel of the car when it crashed into the tree along Adelaide’s Anzac Hwy near Grassmere St about 1pm on Thursday.

The 80-year-old woman in the passenger seat died at the crash site.

The 81-year-old driver was taken to hospital, where he remains in a critical condition.

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The Anzac Hwy remains closed for citybound traffic from Gray St while police examine the scene and investigate the circumstances surrounding the crash.