  Recently we observed a crossover transition (in the Fayet-Iliopoulos
parameter) from weak to strong coupling in N=2 supersymmetric QCD with the U(N)
gauge group and N_f > N quark flavors. At strong coupling this theory can be
described by a dual non-Abelian weakly coupled SQCD with the dual gauge group
U(N_f-N) and N_f light dyon flavors. Both theories support non-Abelian strings.
We continue the study of confinement dynamics in these theories, in particular,
metamorphoses of excitation spectra, from a different side. A number of results
obtained previously are explained, enhanced and supplemented by analyzing the
world-sheet dynamics on the non-Abelian confining strings. The world-sheet
theory is the two-dimensional N=(2,2) supersymmetric weighted CP(N_f-1) model.
We explore the vacuum structure and kinks on the world sheet, corresponding to
confined monopoles in the bulk theory. We show that (in the equal quark mass
limit) these kinks fall into the fundamental representation of the unbroken
global SU(N)\times SU(N_f-N)\timesU(1) group. This result confirms the presence
of "extra" stringy meson states in the adjoint representation of the global
group in the bulk theory. The non-Abelian bulk duality is in one-to-one
correspondence with a duality taking place in the N=(2,2) supersymmetric
weighted CP(N_f-1) model.
