The carjackings and subsequent police pursuit occurred in Frankston in Victoria, and led to the dramatic arrest of a 30-year-old man who is now under police guard in hospital.

Around 4.30pm on Tuesday, a 74-year-old woman was loading groceries into her vehicle in a shopping centre car park, when she was approached by a man.

He allegedly climbed into the passenger seat of her car while armed with a knife and demanded she drive.

Almost 30 minutes later the uninjured woman was dropped off at a service station, and the male drove off in her car.

"The stolen car was found after police were notified that a vehicle had crashed into a pole and the driver had run off," a Victoria Police spokesperson said

At 7.30pm on Tuesday, the same offender allegedly threatened a man in Seaford with a knife before stealing his white Toyota Camry sedan.

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The stolen Toyota was spotted by police just after 11pm, and when officers attempted to intercept the vehicle the driver failed to pull over.

"With assistance from the Air Wing, the car was located and stop sticks were successfully deployed," police said.

Just after midnight the vehicle stopped and the driver ran from the scene. He was arrested by the dog squad nearby.

The man was taken to hospital and is currently under hospital guard.

Anyone with information is urged to call Crime Stoppers on 1800 333 000.