  In this work we study the spectral functions of scalar mesons in one- and
two-channel cases. When the propagators satisfy the K\"allen-Lehman
representation a normalized spectral function is obtained, allowing to take
into account finite-width effects in the evaluation of decay rates. In the
one-channel case, suitable to the light sigma and k mesons, the spectral
function can deviate consistently from a Breit-Wigner shape. In the two-channel
case with one subthreshold channel the evaluated spectral function is well
approximated by a Flatte' distribution; when applying the study to the a_0(980)
and f_0(980) mesons the tree-level forbidden KK decay is analysed.
