 Olaf married Aud the Deep-minded ("Auðr"), daughter of Ketil Flatnose, the ruler of the Hebrides, according to Icelandic traditions ("Landnámabók", "Laxdæla saga").The Irish sources name Olaf's wife only as the daughter of a "King Aedh".Olaf and Auðr had a son, Thorstein the Red ("Þorsteinn rauðr"), who attempted to conquer Scotland in the 870s.