Abstract: The sensitivity and n-sensitivity are studied under directed partial semigroup actions, and some results about them are obtained. First, for an abelian Λ-topological dynamical system (X, T^λ_λ∈Λ) on compact metric space (X, d), if it is a transitive C-system, then it is almost equicontinuous if and only if it is non-sensitive. Se-cond, if (X, T^λ_λ∈Λ)is a Λ-topological dynamical system and X is a locally connected space, then (X, T^λ_λ∈Λ)is sensitive if and only if it is n-sensitive for every n≥2.