We study the convergence of the solutions of a sequence of relaxed Dirichlet prob lems relative to Dirichlet forms to the solution of the Γ -limit problem. In particular we prove the strong convergence in D^P_0[a,Ω](1≤p≤2) and the existence of “correctors” for the strong convergence in D_0[a,Ω] . The above two results are generalizations to our framework of previous results proved in [10] in the usual uniformly elliptic setting.