They are the latest casualties from unexploded ordnance (UXO) in South Kordofan.
Almost three years of war in that state and Blue Nile, where insurgents and the army are also fighting, have displaced or severely affected more than one million people.
"According to reports received, on March 28 a man and a 12-year-old boy were killed by an unexploded ordnance in Abu Kershola town, South Kordofan," the UN's Office for the Coordination of Humanitarian Affairs (OCHA) said in its weekly bulletin.
The fighting displaced more than 60,000 people, many of whom have been returning to Abu Kershola, OCHA said.
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"The area will need to be cleared of all UXOs and mine risk education should be offered to people living in the area," it said.
In July last year nine children were killed by a UXO near Abu Kershola.
The UN's independent expert on human rights in Sudan, Mashood Adebayo Baderin, said during a February visit to the country that UN officers in South Kordofan had emphasised the problem of UXOs and the need for demining.