A scenario is given.for the formation of XI- states and the transition
s to states with double-LAMBDA in anticipation of observations, especi
ally in the KEK-E224 experiment. First, the production cross sections
of XI- hypernuclear states by (K-, K+) reactions are calculated within
the framework of the distorted-wave impulse approximation. Next, the
transition rates from XI- hypernuclear states to possible double-LAMBD
A states are obtained, which are closely related to single- and double
-LAMBDA emissions after the XI-p-->LAMBDALAMBDA conversion in nuclei.