Like his father, King Maelgwn Gwynedd, Rhun was a tall man, hence his nickname. According to Welsh law, Rhun managed to succeed to the Gwynedd throne despite being illegitimate. However, his position was disputed by his eldest legitimate half-sister, St. Eurgain and her husband, Prince Elidyr Mwynfawr (the Wealthy) of Strathclyde. Elidyr's armies invaded Gwynedd. They sailed through the Menai Straits and landed near Caer-Segeint, alias Caer-yn-Arfon (Caernarfon). Rhun had strong local support, however, and the Northern army was thoroughly defeated. Elidyr was killed in battle on the Cadnant Brook. King Riderch Hael (the Generous) of Strathclyde, Elidyr's cousin, appears to have attempted a revenge attack a few years later. Rhun was victorious for a second time, and followed through by taking a large army north to help his half-brother, Bridei, secure his place on the Pictish throne. Rhun's favourite palace was that which he set up up-river from Degannwy at the old Roman fort of Canovium. Originally Caer-Ganwy, it later took the name of Caer-Rhun in his honour. He died there in 586.