The family was the legitimate line of the Hosokawa clan, and the family was successively appointed to the post of kanrei in 'Muromachi bakufu,' as well as being hereditary Shugo daimyo in Settsu Province, Tanba Province and so on.
細川氏の嫡流で、摂津国・丹波国などの守護大名を世襲したと同時に、代々「室町幕府」の管領職に任命を受けた。