Post-mortem examinations are to be carried out on the bodies of a man and a woman found dead separately.
Detectives are investigating the suspicious death of a man in his 20s whose body was discovered in a derelict building in Waterford.
And gardai in Dublin appealed for witnesses when a woman died after a suspected assault outside a fast food outlet.
The grim discovery in Waterford was made at about 6pm in a disused premises in New Street. The scene has been sealed off pending a Garda forensic examination and the State Pathologist has been notified. An incident room has been set up at Waterford Garda Station and gardai have appealed for incidents.
In Dublin a 51-year-old woman named locally as Phyllis Black was attacked outside a chip shop in Parnell Street in the early hours of Sunday. Her body was discovered in her flat in Liberty House, Railway Street, off Lower Gardiner Street, in Dublin's north inner city on Sunday night.
Officers have examined CCTV in the area and have appealed for another woman involved in the altercation at about 3.20am to come forward.
The suspect is described as being in her 20s and wearing a dark jacket, black mini skirt or shorts with black tights and a sparkling top which was possibly pink, and was carrying a black shoulder bag.
It is understood Ms Black either fell or got knocked to the ground, and possibly banged her head. The injured woman went to the Mater Hospital but it is believed she left before receiving any treatment. Ms Black was found dead by a relative who was concerned over her whereabouts when she had not made contact all day.
The post-mortem examination will determine if her death was linked to the incident.
Elsewhere, gardai are continuing to question a 44-year-old man over the death of a woman on Saturday. The 37-year-old woman was discovered at a flat in Upper Sherrard Street in the capital with injures and rushed to the Mater Hospital, were she died.