  The coupled processes -- the pion-pion scattering and pi pi --> K antiK in
the I^GJ^{PC}=0^+0^{++} channel -- are analyzed (both separately and combined)
in a model-independent approach based on analyticity and unitarity and using a
uniformization procedure. It is shown: 1) a structure of the Riemann surface of
the S-matrix for considered coupled processes must be allowed for calculating
both amplitudes and resonance parameters, such as the mass and width; 2) the
combined analysis of coupled processes is needed as the analysis of only pi-pi
channel does not give correct values of resonance parameters even if the
Riemann surface structure is included.
