On the basis of a simultaneous description of the isoscalar s-wave channel of the ππ scattering (from the threshold up to 1.9 GeV) and of the ππ → KK process (from the threshold to ∼ 1.4 GeV) in the model-independent approach, a confirmation of the σ-meson at ∼ 665 MeV and an indication for the glueball nature of the f 0 (1500) state are obtained. It is shown that the large ππ-background, usually obtained, combines, in reality, the influence of the left-hand branch-point and the contribution of a very wide resonance at ∼ 665 MeV. The coupling constants of the observed states with the ππ and KK systems and lengths of the ππ and KK scattering are obtained.