The C-oscillation due to Martin-Löf shows that {α| ∀ n [C(α n)≥ n-O(1)]=, which also follows {α| ∀ n [K(α n)≥ n+K(n)-O(1)]=. By generalizing them, we show that there does not exist a real α such that ∀ n (K(α n)≥ n+λ K(n)-O(1)) for any λ>0.