In the first incident, a 23-year-old man from Clonmel, Co Tipperary was left with severe head injuries at Gladstone Street in the town centre where a passer-by found him lying on the ground shortly before 3am yesterday.
He was being treated at Cork University Hospital where his condition was described as critical.
In Kingscourt, Co Cavan, gardaí were working on a number of theories to explain how a 28-year-old man was left fighting for his life after suffering serious injuries in the town.
The young steel worker was discovered unconscious on the roadside near his home at Rock Road at about 3.30am.
Sergeant Earnan Gilleran from Baileboro Garda station who is heading the investigation appealed for anyone who was in the vicinity of Rock Road between 2am and 3.30am on Monday to contact the Gardaí at Kingscourt on 042-9667292 or Baileboro on 042-9694570.
Meanwhile, the family of a 20-year-old Dublin man who has been in a coma since suffering severe injuries in a mystery incident at a garda station in the city maintained their anxious vigil last night.
His family has rejected the official explanation that he attempted suicide in his cell at the station and believe he was the victim of an assault. They are calling for a public inquiry and have instructed solicitors to take action against the State.