[en] We report on a measurement of the differential and total cross sections of inclusive production of Ξ^* resonances in Σ^--nucleus collisions at 345 GeV/c. The cross section for inclusive Ξ⁰₁₅₃₀ production is about a factor of 5 below that of Ξ^-₁₃₂₀ hyperons. The products of cross section and branching ratio for the observed channels Ξ⁰₁₆₉₀→Ξ^-π⁺, Ξ^-₁₈₂₀→Ξ⁰₁₅₃₀π^- a nd Ξ^-₁₉₅₀→Ξ⁰₁₅₃₀π^- are lower by yet another order of magnitude. The Ξ^-₁₈₂₀ and Ξ^-₁₉₅₀ resonances show significantly harder x_F and p_t distributions than Ξ^- and Ξ⁰₁₅₃₀ hyperons. A comparison of the x_F-distribution to PYTHIA and QGSM predictions provides only a partial agreement. (orig.)