In this paper, we characterize the symbols for (semi-)commuting dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space. We show that for φ ,ψ ∈ W1, ∞, SφSψ = SψSφ on (Dh)⊥ if and only if φ and ψ satisfy one of the following conditions: (1) Both φ and ψ are harmonic functions; (2) There exist complex constants α and β, not both O, such that φ = αφ+β.