[en] The 2-point function of the O(N)-symmetric non-linear σ-model in two dimensions is large-N expanded and renormalized, neglecting terms of O(1/N²). At finite cut-off, universal, analytical expressions relate the magnetic susceptibility and the dressed mass to the bare coupling. Removing the cut-off, a similar relation gives the renormalized coupling as a function of the mass gap. In the weak coupling limit these relations reproduce the results of renormalization group improved weak coupling perturbation theory to two-loop order. The constant left unknown, when the renormalization group is integrated, is determined here. The approach to asymptotic scaling is studied for various values of N. (orig.)