Duncan was the grandson of King Malcolm II (ruled 1005–34), who irregularly made him ruler of Strathclyde when that region was absorbed into the Scottish kingdom (probably shortly before 1034). Malcolm violated the established system of succession whereby the kingship alternated between two branches of the royal family. Upon Malcolm's death, Duncan succeeded peacefully, but he soon faced the rivalry of Macbeth, Mormaor (subking) of Moray, who probably had a better claim to the throne. Duncan besieged Durham unsuccessfully in 1039 and in the following year was murdered by Macbeth. Duncan's elder son later killed Macbeth and ruled as King Malcolm III Canmore (1058–93).