He and Airgeatmhar had killed Ailill Finn, who was then High King, only for Ailill's son Eochaid to hold onto the kingship. Eochaid witheld their attacks, and tried to discuss peace with Duach. Duach, however, betrayed and murdered him, and Airgeatmhar took the kingship. Duach later overthrew Airgeatmhar with the aid of Eochaid's son Lugaid Laigde, and took the throne himself. (Wikipedia.org)