G. Benfatto, A. Giuliani, V. Mastropietro Low temperature analysis of two dimensional Fermi systems with symmetric Fermi surface (876K, Postscript) ABSTRACT. We prove the convergence of the perturbative expansion, based on Renormalization Group, of the two point Schwinger function of a system of weakly interacting fermions in two dimensions, with symmetric Fermi surface and up to exponentially small temperatures, close to the expected onset of superconductivity.