[en] A search for baryonia with open and hidden strangeness decaying into strange particles has been carried out in a neutron beam with a mean momentum of 40 GeV/c with the BIS-2 spectrometer at the Serpukhov accelerator. There is a strong indication of the existence of baryonia with negative (M_s) and positive (M-bar_s) strangeness, decaying respectively into Λp-bar + pions and Λ-barp + pions. The isotopic spin of the strange baryonia is ≥ 3/2. Their mean mass is (3060 ±5 (st.) ± 20 (syst.)) MeV/c². There is an indication of the existence of narrow baryonium with hidden strangeness (M_φ), decaying into Λp-barK⁺(+π^±), Λ-barpK^-(+π^±) and K⁰_spp-barK^±. The mean value of its mass is (3260 ±5 (st.) ±20 (syst.)) MeV/c². The widths of the searched baryonia are (35 ± 5) MeV/c^. The production cross-sections the baryonia in the kinematic region X_F ≥0.2 and P_t ≤ 1 GeV/c, are (0.3 - 1.0) μb/per nucleon (90% C.L.). 33 refs.; 9 figs.; 4 tabs