The founder of the family was Mitsuyuki HOSOKAWA, the youngest brother of Yoriyuki, and a post of Shugo was successively taken over to Yorishige HOSOKAWA, Ujihisa HOSOKAWA and to Katsuhisa HOSOKAWA.
頼之の末弟・細川満之を祖とし、細川頼重、細川氏久、細川勝久と代々守護職を継承した。