PoliceScotland say a woman, 39, was attacked in the car park of University Crosshouse Hospital in Kilmarnock at 7.45pm on Thursday.
A second woman, 24, was fatally stabbed at about 8.05pm on Portland Street, about two miles away.
Enquiries carried out so far have indicated that the incidents were linked and an investigation is under way to establish the exact circumstances of what happened.
Officers are not looking for anyone else as part of their investigation and say there is no ongoing threat to the public.
It is understood the incidents are not being treated as terror-related.
A man, 40, then died in a road crash on the C50, on the outskirts of the town, at about 8.30pm
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