The Onin War completely eclipsed shogunal authority and stripped the bakufu of much of its power, but the Shogun was able to hold onto some measure of de facto authority through his military power.
応仁の乱で将軍の権威は完全に失墜し幕府の権力は衰退したが、将軍の軍事的な実権はある程度保たれていた。