The crash happened at 11.20am on the Inverkip Road in Greenock and involved a red Hyundai and a grey Ford Focus.
Police Sergeant Roy McCarney said: "A 79-year-old man who was the passenger of the red Hyundai attended hospital the following day but sadly passed away on November 5.
“The drivers of both vehicles were not injured.
“We are supporting this man’s family during this difficult time and continuing with enquiries to establish the full circumstances.”
Anyone with information should contact police on 101, quoting reference 1365 of October 31.
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