For a pure bounded rationally cyclic subnormal operator S on a separable complex Hilbert space H, Conway and Elias (1993) shows that clos(σ(S) \ σe(S)) = clos(Int(σ(S))). This paper examines the property for rationally multicyclic (N-cyclic) subnormal operators. We show: (1) There exists a 2-cyclic irreducible subnormal operator S with clos(σ(S) \ σe(S)) = clos(Int(σ(S))).(2) For a pure rationally N −cyclic subnormal operator S on H with the minimal normal extension M on K ⊃ H, let Km = clos(span{(M * ) k x : x ∈ H, 0 ≤ k ≤ m}. Suppose M |K N −1 is pure, then clos(σ(S) \ σe(S)) = clos(Int(σ(S))).interior, clos(A) for its closure, A c for its complement, andĀ = {z : z ∈ A}. For λ ∈ C and δ > 0, we set B(λ, δ) = {z : |z − λ| < δ} and D = B(0,