  The $\Lambda$ and neutron decay widths of $\Xi$ hypernuclear states, based on
calculated $\Xi N \to \lala$ mixing amplitudes, are estimated. The widths which
result from using the Nijmegen Model D interaction are sufficiently small, of
order 1.5 MeV, that experiments to observe $\Xi$ hypernuclear states using the
$(K^-,K^+)$ reaction may be feasible.
