[en] A scenario is given for the formation of Ξ^- states and the transitions to states with double-Λ in anticipation of observations, especially in the KEK-E224 experiment. First, the production cross sections of Ξ^- hypernuclear states by (K^-, K⁺) reactions are calculated within the framework of the distorted-wave impulse approximation. Next, the transition rates from Ξ^- hypernuclear states to possible double-Λ states are obtained, which are closely related to single- and double-Λ emissions after the Ξ^-p→ΛΛ conversion in nuclei. (author)