Evidence of azimuthal asymmetries in the time structure and signal size have been found in non-vertical showers at the Pierre Auger Observatory. It has been previously shown that the asymmetry in time distributions offers a new possibility for the determination of the mass composition. New studies have demonstrated that the dependence of the asymmetry parameter in the rise-time and fall-time distributions with secθ shows a clear peak. Both, the position of the peak, Xasymax, and the size of the asymmetry at Xasymax are sensitive to primary mass composition and have a small dependence on energy. In this paper a study of the discriminating power of the new observables to separate primary species is presented.