The structure of the ( I = 0, J PC = 0 ++) S-wave ππ-amplitude up to an invariant energy of 1.15 GeV is determined from a simultaneous analysis of the GAMS data on the π − p → π 0 π 0 n reaction in a set of 4-momentum transfer squared intervals, together with the S-wave ππ phase shift (CERN-Munich data) and the Crystal Barrel data on the p p → π 0π 0π 0 , p p → ηηπ 0 and p p → ηπ 0π 0 annihilations at rest. The analysis shows the existence of two resonances near the K K threshold: a narrow one with a mass of 987 MeV and a width of 80 MeV, and a wide one with a mass of 1160 MeV and a width about 900 MeV. These physical states appear as a result of mixing of two original states with masses ≈ 800 MeV and ≈ 1200 MeV. The first one is a candidate for the σ-resonance.