Police said the men, aged 18 and 35, were involved in a disturbance in Cambusdoon Road in Craigend at about 0430 BST on Saturday.
They are treating the attack on the younger man as attempted murder and the second incident as serious assault.
Hospital staff said the 18-year-old's condition was "serious" and the 35-year-old was "serious but stable".
Det Sgt Eddie Waye said: "I would appeal to anyone who may have been in the area at the time and who may have witnessed a disturbance to come forward."
Anyone with any information which might help police with their inquiries is asked to contact Easterhouse CID on 0141 532 4316.
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