Let G be a bounded simply connected domain in the complex plan with boundary ?G=Γ∈C(1,α),0<α<1 . In this paper we estimate the uniform and mean approximation orders of functions in A(G) and Ｅｑ（Ｇ）（１＜ｑ＜＋∞）by their Lagrange in terpolation rational functions based on the zeros of the generalized Faber-Dzerbasejan rational functions with preassigned poles in the exterior of G.
