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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].