  It is shown that the new data on the excitation energy Eex spectrum of the
residual nuclear system in the Sigma-hypernuclear region in the reactions
(K-,pi+-) on Be-9 and in the reaction (K-,pi+) on He-4 and C-12 can be
described without the supposition on the existence of excited
Sigma-hypernuclear states. The basis is formed by a simultaneous consideration
of the quasi-free Sigma production and Sigma-nuclear rescattering (elastic and
with Sigma -> Lambda conversion) with account of interference of the respective
amplitudes. For final decision of the question about the nature of the
irregularities in Eex spectrum, it is proposed to study the picture
corresponding to the so-called moving complex singularity of the triangle graph
with Sigma rescattering: the position and the width of the peak in Eex
distribution must appreciably change with momentum transferred from the initial
kaon to the final pion.
