Some of the other emperors after the Emperor Saga also demoted their family members to being their subjects by giving them the surname of Minamoto and those Minamoto clan who were descended from the Emperor Saga called themselves Saga-Genji and afterwards, the Minamoto clan took their parental emperors' names as their clan's surnames (such as Ninmyo-Genji, Montoku-Genji, Seiwa-Genji and Uda-Genji).
嵯峨天皇の後の天皇も度々皇族を源氏として臣籍に下したことから、嵯峨天皇を祖とする源氏を嵯峨源氏と称する様になり、以後源氏はそれぞれの祖と仰ぐ天皇の号をもって氏族の称とした（仁明源氏、文徳源氏、清和源氏、宇多源氏など）。