Apparently, Naritsuna also followed the Kamakura bakufu (Japanese feudal government headed by a shogun) because Naritsuna's elder brother, MINAMOTO no Aritsuna, joined MINAMOTO no Yoritomo when Yoritomo rose up in arms (the place name 'OIGAWA village' in Atsugi City, Kanagawa Prefecture, seems to have had a relationship with Naritsuna or Naritsuna's son Mitsutsuna OIKAWA, but formerly it was also written as '及河' and was properly read as 'OIGAWA' in a dull sound.
成綱の兄・源有綱は源頼朝の挙兵の際に参陣していることから、成綱もまた鎌倉幕府に従ったと思われる（神奈川県厚木市の「及川村」という地名は成綱または成綱の子・及川光綱の縁かとも思われるが、古くは「及河」とも書き「おいがわ」と濁って読むのが正しい。