[en] The results of methodical investigations on separation of the channels with one neutral particle in K^-p interactions at 32 GeV/c are given. On the basis of the calculations according to the GRIND program separated are the following exclusive reactions: K^-p→K^-p+m(π⁺π^-)+π⁰, K^-p→ anti Ksub(visible)sup(0)pπsup(-) + m(π⁺π^-)+π⁰, K^-p→π^-p(+mπ⁺π^-)+ anti Ksub(visible)sup(0), K^-p→K^-π⁺+m(π⁺π^-)+N, where m=0, 1, 2. The reaction cross section with π⁰, Ksub(visible)sup(0) and N particles are estimated. The dependence of the reaction cross sections on energy is given. The accuracy of measurement of the particle kinematic parameters in the K^-p interactions permits rather reliably separate the exclusive channels with one invisible π^- meson at > 2 charged particle multiplicity. Separation of the channels with invisible K⁰ meson is impeded by great admixtures from kinematically indistinguishable processes with one or two π⁰ mesons and relatively small cross section of these channels. The energy dependence of the channel cross sections with one π⁰ meson in 4- and 6-ray events is analogous to the behaviour of the cross sections of the corresponding channels without π⁰ meson at Psub(labor) > 10 GeV/c