According to tradition , the two lines , the Agiads and Eurypontids , were respectively descended from the twins Eurysthenes and Procles , the descendants of Heracles who supposedly conquered Sparta two generations after the Trojan War .
According to tradition , the two lines , the Agiads and Eurypontids , were descended from the twins Eurysthenes and Procles . These twins were said to be the descendants of Heracles , who conquered Sparta two generations after the Trojan War .