In this note we study radicals of skew polynomial ring R[x; α] and skew Laurent polynomial ring R[x, x −1; α], for a skew-Armendariz ring R. In particular, among the other results, we show that for an skew-Armendariz ring R, J(R[x; α]) = N 0(R[x; α]) = Nil*(R)[x; α] and J(R[x, x −1; α]) = N 0(R[x, x −1; α]) = Nil*(R)[x, x −1; α].