Abstract : Let a symbol σ x, ξ belongs to the class S 1, 1, δ 1, δ 2 0, 0 with x, ξ ∈ ℝ n 1 × ℝ n 2 and 0 ≤ δ 1, δ 2 < 1 . This paper mainly establish the boundedness of the class of all bi-parameter pseudo-differential operators associated with the symbol σ x, ξ on the multi-parameter non-homogeneous Besov-Lipschitz and Triebel-Lizorkin spaces.