  We present the results of simultaneous analysis of the S-wave pi pi-spectra
in the reactions pi^- p -> (pi^0 pi^0)_S n at p_{lab}=38 GeV/c (GAMS) and pi^-
p -> (pi^+ pi^-)_S n at p_{lab}=18 GeV/c (E852 Collaboration) at moderate
momenta transferred to the nucleon, |t| < 1.5 (GeV/c)^2. The t-distributions
are described by the reggeized pi- and a_1-exchanges provided by the leading
and daughter trajectories, while the M_{pi pi}-spectra are determined by a set
of scalar-isoscalar resonances. With M_{pi pi}-distributions averaged over
t-intervals, we have found several solutions given by different t-channel
exchange mechanisms at |t| ~ (0.5-1.5) (GeV/c)^2, with resonance parameters
close to each other. We conclude that despite a poor knowledge of the structure
of the t-exchange, the characteristics of resonances such as masses and widths
can be reliably determined using the processes under discussion. As to pole
positions, we have found (1031 +/- 10) - i(35 +/- 6) MeV for f_0(980) and (1315
+/- 20) - i(150 +/- 30) MeV for f_0(1300).
