  For the first time, as far as we know, in field theory are found explicit
forms of propagators satisfying the K\"allen -- Lehmann representation. To be
exact, it is shown that scalar meson propagators, taking into account a virtual
intermediate state contribution to the resonance self-energy, satisfy the
K\"allen -- Lehmann representation in the wide domain of coupling constants of
the light scalar mesons with the two-particle states. It is proposed to use
these propagators in routine fitting data about light scalar mesons to reveal
physics underlying the light scalar mesons.
