Like the Ashikaga family positioned to accede to the shogunate, the Hosokawa clan was related to the linage of the Ashikaga clan and bore the role of kanrei alternately with the Shiba and the Hatakeyama clans in the same family linage of the Ashikaga family like the Hosokawa clan.
細川氏は足利将軍家同様、足利氏の流れを汲み、同じく将軍家と同族である斯波氏、畠山氏とともに、管領職を持ち回りで司ってきた。