[en] Using the impulse model approximation, the cross sections are determined for the reactions K^-n → Λ⁰π^-π⁰, and K^-n → Σ⁰π^- in the center-of-mass range from 1500 to 1600 MeV. The angular distributions for the Λ⁰π^- and Σ⁰π^- final states are also presented. Based on an energy-dependent partial-wave analysis of the reactions K^-n → Λ⁰π^- and K^-n → Σ⁰π^-, it is found that the data can be represented using only background terms plus the known D13(1670) and D15(1765) resonance states. The presence of a small fraction (<20%) of nonimpulsive events is explained mainly as a result of final-state interactions; in particular, a peak observed in the mass distribution of the Λp dibaryon system at about 2130 MeV is suggested as possible evidence of final-state interactions which give rise to nonimpulsive reactions