  A joint analysis of the pi+pi- and pi0pi0 S-wave amplitudes including results
of three experiments has been performed. Using our theoretical model of the
pion-pion production in which not only the pion exchange but also the a1(1260)
meson exchange were taken into account we have obtained a unique solution
(called "down-flat") for the scalar-isoscalar phase shifts. Thus a
long-standing problem of ambiguities in the S-wave isoscalar amplitude has been
finally resolved and the second ("up-flat") solution was eliminated.
