  We investigate the production of a cascade hyperon ($\Xi$) and bound $\Xi^-$
hypernuclei in the $(K^-,K^+)$ reaction on proton and nuclear targets,
respectively, within a covariant effective Lagrangian model. The $K^+\Xi^-$
production vertex is described by excitation, propagation and decay of
$\Lambda$ and $\Sigma$ resonance states in the initial collision of a $K^-$
meson with a free or bound proton in the incident channel. The parameters of
the resonance vertices are taken from previous studies and SU(3) symmetry
considerations. The model is able to provide a good description of the
available data on total and differential cross sections for the $p(K^-,
K^+)\Xi^-$ reaction. The same mechanism was used to describe the hypernuclear
production reactions $^{12}$C$(K^-,K^+)^{12}{/!/!/!_{/Xi^-}}$Be and
$^{28}$Si$(K^-,K^+)^{28}{/!/!/!_{\Xi^-}}$Mg, where $\Xi$ bound state spinors
calculated within a phenomenological model have been employed. Both the
elementary and hypernuclear production cross sections are dominated by the
contributions from the $\Lambda$(1520) intermediate resonant state. The beam
momentum dependence of the $0^\circ$ differential cross sections for the
formation of the $\Xi$ hypernuclei is found to be remarkably different from
what has been observed previously in the impulse approximation model
calculations
