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For a ring R with an automorphism α an n-additive mapping D:Rn→ R is called a skew n-derivation w.r.t. α if it is an α-derivation of R for each argument. Namely it is always an α-derivation of R for the argument being left once (n-1) arguments are fixed by (n-1) elements in R. In the present note, begin with a result of Park [9], we prove that if a skew n-derivation D associated with an automorphism α with trace τ of a noncommutative n! torsion free semiprime ring R satisfying [τ(x), α(x)] ∈ Z(R) for all x ∈ I, then [τ(x), α(x)]=0 for all x ∈ I, a nonzero ideal of R. Moreover, we investigate the commutativity in case of prime rings. [ABSTRACT FROM AUTHOR]