  In most of the Nambu:Jona-Lasinio(NJL)-type models, realizing the hidden
chiral symmetry, the existence of a scalar particle \sigma is needed with a
mass m_\sigma=2 m_q, as a partner of the Nambu-Goldstone boson \pi. However,
the results of many analyses on \pi\pi phase-shift thus far made have been
negative for its existence. In this paper we re-analyze the phase-shift,
applying a new method, the interfering amplitude method, which treats the
T-matrix directly and describes multi-resonances in conformity with the
unitarity. As a result, the existence of \sigma has been strongly suggested
from the behavior of the \pi\pi-->\pi\pi phase shift between the \pi\pi- and
the KK- thresholds, with mass = 553.3 +- 0.5_{st} MeV and width= 242.6 +-
1.2_{st} MeV. The most crucial point in our analysis is the introduction of a
negative background phase, possibly reflecting a ``repulsive core" in \pi\pi
interactions. The properties of f_0(980) are also investigated from data
including those over the KK threshold. Its mass is obtained as 993.2 +-
6.5_{st} +- 6.9_{sys} MeV. Its width is about a hundred MeV, although this
depends largely on the treatment of the elasticity and the \pi\pi-->KK phase
shift, both of which may have large experimental uncertainties.
