A blue Dacia Sandero mounted a kerb on the A4106 Tythegston road, just before the A48 roundabout, and struck the 19-year-olds at about 16:00 BST on Friday.
The critically injured man has been flown by air ambulance to University Hospital of Wales, Cardiff.
A 49-year-old driver of the Dacia is helping officers from South Wales Police with their enquires.
The second injured man, understood to be less seriously hurt, is being treated at the Princess of Wales Hospital in Bridgend.
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